##### Unit Test 2 Probabilty

What is the probability of an event that is certain to occur?

A) 0.5

B) 0.95

C) 0.99

D) 1

D) 1

What is the probability of an impossible event?

A) 1

B) 0.1

C) -1

D) 0

D) 0

Which of the following cannot be a probability?

A) 2/3

B) 5/3

C) 3/5

D) 1/2

B) 5/3

greater than one

On a multiple choice test with four possible answers for each
question, what is the probability of answering a question correctly if
you make a random guess?

A) 1/4

B) 1

C) 3/4

D) 1/2

A) 1/4

A bag contains 6 red marbles, 3 blue marbles, and 5 green marbles. If
a marble is randomly selected

from the bag, what is the
probability that it is blue?

A) 1/11

B) 1/3

C) 3/14

D) 1/5

C) 3/14

3/(6+3+5)

Two 6-sided dice are rolled. What is the probability that the sum of
the two numbers on the dice will be 5?

A) 8/9

B) 5/6

C) 1/9

D) 4

C) 1/9

4/36

A class consists of 67 women and 12 men. If a student is randomly
selected, what is the probability that the student is a woman?

A) 1/79

B) 12/79

C) 67/12

D) 67/79

D) 67/79

67 women/(67w+12m)

In a certain class of students, there are 12 boys from Wilmette, 3
girls from Kenilworth, 9 girls from Wilmette, 6 boys from Glencoe, 2
boys from Kenilworth and 6 girls from Glencoe. If the teacher calls
upon a student to answer a question, what is the probability that the
student will be from Kenilworth?

A) 0.132

B) 0.079

C) 0.172

D) 0.1

A) 0.132

(kenilworth 3g + 2b)/ (12+3+9+6+2+6)

5/28

Find the indicated complement.

Based on meteorological records,
the probability that it will snow in a certain town on January 1st is
0.148. Find the probability that in a given year it will not snow on
January 1st in that town.

A) 0.852

B) 6.757

C) 0.174

D) 1.148

A) 0.852

1-.148

Find the indicated probability.

A spinner has equal regions
numbered 1 through 15.What is the probability that the spinner will
stop on an even number or a multiple of 3?

A) 2/3

B) 1/2

C) 7/9

D) 1/3

A) 2/3

2/3/4/6/8/9/10/12/14/15 = 10

10/15

If you pick a card at random from a well shuffled deck, what is the
probability that you get a face card or a spade?

A) 11/26

B) 9/26

C) 1/22

D) 25/52

A) 11/26

(26 spades + 9 face cards)/52

The table describes the smoking habits of a group of asthma
sufferers.

If one of the 1124 people is randomly selected, find the
probability that the person is a man or a heavy smoker.

A) 0.483

B) 0.516

C) 0.549

D) 0.514

B) 0.516

(545 men + 35 heavy smoking women)/1124

Of the 73 people who answered "yes" to a question, 14 were
male. Of the 53 people that answered "no" to the question, 9
were male. If one person is selected at random from the group, what is
the probability that the person answered "yes" or was male?

A) 0.192

B) 0.183

C) 0.651

D) 0.762

C) 0.651

(73 yes + 9 no male)/(73+53)

A 6-sided die is rolled. Find P(3 or 5).

A) 1/36

B) 1/6

C) 1/3

D) 2

C) 1/3

A bag contains 6 red marbles, 2 blue marbles, and 1 green marble.
Find P(not blue).

A) 7

B) 2/9

C) 7/9

D) 9/7

C) 7/9

Find the probability of correctly answering the first 2 questions on
a multiple choice test if random guesses are made and each question
has 5 possible answers.

A) 1/32

B) 5/2

C) 1/25

D) 2/5

C) 1/25

(1/5)*(1/5)

A manufacturing process has a 70% yield, meaning that 70% of the
products are acceptable and 30% are defective. If three of the
products are randomly selected, find the probability that all of them
are acceptable.

A) 0.027

B) 2.1

C) 0.343

D) 0.429

C) 0.343

.7^{3}

A bin contains 60 light bulbs of which 5 are defective. If 4 light
bulbs are randomly selected from the bin with replacement, find the
probability that all the bulbs selected are good ones. Round to the
nearest thousandth if necessary.

A) 0.917

B) 0.706

C) 0.726

D) 0

B) 0.706

(55/60)^{4}

When a pair of dice are rolled there are 36 different possible
outcomes: 1-1, 1-2, ... 6-6. If a pair of dice are rolled 5 times,
what is the probability of getting a sum of 5 every time? Round to
eight decimal places.

A) 0.00032

B) 0.04

C) 0.00001694

D) 0.00005168

C) 0.00001694

1-4,4-1,2-3,3-2 = 4

(4/36)^{5}

In a homicide case 7 different witnesses picked the same man from a
line up. The line up contained 5 men. If the identifications were made
by random guesses, find the probability that all 7 witnesses would
pick the same person.

A) 0.0000595

B) 1.4

C) 0.0000128

D) 0.000064

C) 0.0000128

(1/5)^{7}

You are dealt two cards successively (without replacement) from a
shuffled deck of 52 playing cards. Find the probability that both
cards are black. Express your answer as a simplified fraction.

A) 1/2652

B) 13/51

C) 25/102

D) 25/51

C) 25/102

(26/52)*(25/51)

You are dealt two cards successively (without replacement) from a
shuffled deck of 52 playing cards. Find the probability that the first
card is a King and the second card is a queen. Express your answer as
a simplified fraction.

A) 2/13

B) 1/663

C) 13/102

D) 4/663

D) 4/663

(4/52)*(4/51)

What is the probability that 4 randomly selected people all have
different birthdays? Round to four decimal places.

A) 0.9836

B) 0.9891

C) 0.9918

D) 0.9729

A) 0.9836

1*(364/365)*(363/365)*(362/365)

A IRS auditor randomly selects 3 tax returns from 55 returns of which
6 contain errors.What is the probability that she selects none of
those containing errors? Round to four decimal places.

A) 0.7071

B) 0.0013

C) 0.7023

D) 0.0008

C) 0.7023

(49/55)*(48/54)*(47/53)

Provide a written description of the complement of the given event.

When 100 engines are shipped, all of them are free of defects.

A) None of the engines are defective.

B) At most one of
the engines is defective.

C) All of the engines are defective.

D) At least one of the engines is defective.

D) At least one of the engines is defective.

Provide a written description of the complement of the given event.

When several textbooks are edited, none of them are found to be
free of errors.

A) All of the textbooks are free of errors.

B) One of the
textbooks is free of errors.

C) At most one of the textbooks is
free of errors.

D) At least one of the textbooks is free of errors.

D) At least one of the textbooks is free of errors.

Find the indicated probability. Round to the nearest thousandth.

An unprepared student makes random guesses for the ten
true-false questions on a quiz. Find the

probability that there
is at least one correct answer.

A) 0.999

B) 0.100

C) 0.900

D) 0.001

A) 0.999

1-(.5^{10})

Find the indicated probability. Round to the nearest thousandth.

A sample of 4 different calculators are randomly selected from a
group containing 18 that are defective and 37 that have no defects.
What is the probability that at least one of the calculators is
defective?

A) 0.806

B) 0.795

C) 0.180

D) 0.194

A) 0.806

1- [(37/55)*(36/54)*(35/53)*(34/52)]

Find the indicated probability.

The table shows the soft
drinks preferences of people in three age groups.

If one of the 255 subjects is randomly selected, find the
probability that the person is over 40 years of age given that they
drink root beer.

A) 5/17

B) 6/17

C) 2/5

D) None of the above is correct.

C) 2/5

30 men drinking rootbeer / (25+20+30) total rootbeer

The table describes the smoking habits of a group of asthma
sufferers.

If one of the 1026 subjects is randomly selected, find the
probability that the person chosen is a nonsmoker given that it is a
woman. Round to the nearest thousandth.

A) 0.543

B) 0.379

C) 0.706

D) 0.437

C) 0.706

389 NSwomen /551 women

There are 13 members on a board of directors. If they must form a
subcommittee of 5 members, how many different subcommittees are
possible?

A) 120

B) 371,293

C) 1287

D) 154,440

C) 1287

13 nCr 5

The library is to be given 7 books as a gift. The books will be
selected from a list of 16 titles. If each book selected must have a
different title, how many possible selections are there?

A) 57,657,600

B) 11,440

C) 112

D) 268,435,456

B) 11,440

16 nCr 7

The organizer of a television show must select 5 people to
participate in the show. The participants will be selected from a list
of 24 people who have written in to the show. If the participants are
selected randomly, what is the probability that the 5 youngest people
will be selected?

A) 1/5100480

B) 1/120

C) 1/42,504

D) 1/3

C) 1/42,504

numerator = 1

denominator = 24 nCr 5

How many 3-digit numbers can be formed using the digits 1, 2, 3, 4,
5, 6, 7 if repetition of digits is not allowed?

A) 210

B) 6

C) 5

D) 343

A) 210

7 nPr 3

How many ways can 6 people be chosen and arranged in a straight line
if there are 8 people to choose from?

A) 20,160

B) 40,320

C) 720

D) 48

A) 20,160

8 nPr 6

There are 9 members on a board of directors. If they must elect a
chairperson, a secretary, and a treasurer, how many different slates
of candidates are possible?

A) 729

B) 84

C) 504

D) 362,880

C) 504

9 nPr 3

A tourist in France wants to visit 5 different cities. If the route
is randomly selected, what is the probability that she will visit the
cities in alphabetical order?

A) 120

B) 1/5

C) 1/25

D) 1/120

D) 1/120

1/ (5!)

The number of oil spills occurring off the Alaskan coast

A) Continuous

B) Discrete

B) Discrete

The braking time of a car

A) Continuous

B) Discrete

A) Continuous

Find the mean of the given probability distribution.

A) μ = 2.53

B) μ = 2.43

C) μ = 2.39

D) μ = 2.29

C) μ = 2.39

L1 & L2 run = Σx

Find the mean of the given probability distribution.

The probabilities that a batch of 4 computers will contain 0, 1,
2, 3, and 4 defective computers are 0.5729, 0.3424, 0.0767, 0.0076,
and 0.0003, respectively. Round answer to the nearest hundredth.

A) μ = 0.42

B) μ = 0.52

C) μ = 2.00

D) μ = 1.09

B) μ = 0.52

L1 & L2 run = Σx

Find the standard deviation for the given probability distribution.

A) σ = 1.45

B) σ = 1.41

C) σ = 2.91

D) σ = 1.99

B) σ = 1.41

L1 & L2 run = σx

A police department reports that the probabilities that 0, 1, 2, and
3 burglaries will be reported in a given day are 0.49, 0.38, 0.10, and
0.03, respectively. Find the standard deviation for the probability
distribution. Round answer to the nearest hundredth.

A) σ = 1.04

B) σ = 0.78

C) σ = 0.60

D) σ = 1.02

B) σ = 0.78

L1 & L2 run = σx

Focus groups of 11 people are randomly selected to discuss products
of the Famous Company. It is determined that the mean number (per
group) who recognize the Famous brand name is 6.2, and the standard
deviation is 0.51. Would it be unusual to randomly select 11 people
and find that greater than 9 recognize the Famous brand name?

A) Yes

B) No

A) Yes

6.2+(.51*2)

Assume that a researcher randomly selects 14 newborn babies and
counts the number of girls selected, x. The probabilities
corresponding to the 14 possible values of x are summarized in the
given table. Answer the question using the table.

Find the probability of selecting exactly 8 girls.

A) 0.122

B) 0.000

C) 0.183

D) 0.022

C) 0.183

Assume that a researcher randomly selects 14 newborn babies and
counts the number of girls selected, x. The probabilities
corresponding to the 14 possible values of x are summarized in the
given table. Answer the question using the table.

Find the probability of selecting 12 or more girls.

A) 0.006

B) 0.022

C) 0.007

D) 0.001

C) 0.007

.006+.001+0

A contractor is considering a sale that promises a profit of $20,000
with a probability of 0.7 or a loss (due to bad weather, strikes, and
such) of $14,000 with a probability of 0.3. What is the expected
profit?

A) $9800

B) $6000

C) $14,000

D) $23,800

A) $9800

-14000*.3 = -4200

20000*.7 = 14000

14000-4200

Suppose you pay $2.00 to roll a fair die with the understanding that
you will get back $4.00 for rolling a 2 or a 4, nothing otherwise.
What is your expected value?

A) -$2.00

B) $4.00

C) -$0.67

D) $2.00

C) -$0.67

-2*.666 = -1.33

4-2*.333 = .66

.66-1.33

Suppose you buy 1 ticket for $1 out of a lottery of 1,000 tickets
where the prize for the one winning ticket is to be $500.What is your
expected value?

A) $0.00

B) -$0.40

C) -$1.00

D) -$0.50

D) -$0.50

-1*.999 = -.999

(500-1)*.001 = .499

.499-.999

A 28-year-old man pays $200 for a one-year life insurance policy with
coverage of $120,000. If the probability that he will live through the
year is 0.9994, what is the expected value for the insurance policy?

A) -$128.00

B) -$199.88

C) $119,928.00

D) $72.00

A) -$128.00

-200*.9994 = -199.88

119800*.0006 = 71.88

71.88-199.88

Determine whether the given procedure results in a binomial
distribution. If not, state the reason why.

Choosing 7 marbles from a box of 40 marbles (20 purple, 12 red,
and 8 green) one at a time without replacement, keeping track of the
number of red marbles chosen.

A) Procedure results in a binomial distribution.

B) Not
binomial: the trials are not independent.

C) Not binomial: there
are more than two outcomes for each trial.

D) Not binomial:
there are too many trials.

B) Not binomial: the trials are not independent.

*without replacement

1. The has fixed number of trials

2. The trials must be
independent

3. out comes classified into two categories (success
or failure

4. The probability of success remains the same in all trials

Determine whether the given procedure results in a binomial
distribution. If not, state the reason why.

Choosing 6 marbles from a box of 40 marbles (20 purple, 12 red,
and 8 green) one at a time with replacement, keeping track of the
number of red marbles chosen.

A) Procedure results in a binomial distribution.

B) Not
binomial: the trials are not independent.

C) Not binomial: there
are more than two outcomes for each trial.

D) Not binomial:
there are too many trials.

A) Procedure results in a binomial distribution.

1. The has fixed number of trials

2. The trials must be
independent

3. out comes classified into two categories (success
or failure

4. The probability of success remains the same in all trials

A test consists of 10 true/false questions. To pass the test a
student must answer at least 6 questions correctly. If a student
guesses on each question, what is the probability that the student
will pass the test?

A) 0.172

B) 0.828

C) 0.205

D) 0.377

D) 0.377

Use binomcdf

trials = 10

P = .5

X = 5

= .623

1 - .623 = .377

Find the probability of at least 2 girls in 10 births. Assume that
male and female births are equally likely and that the births are
independent events.

A) 0.945

B) 0.989

C) 0.044

D) 0.011

B) 0.989

Use binomcdf

trials = 10

P = .5

X = 1

= .011

1 - .011 = .989

An airline estimates that 90% of people booked on their flights
actually show up. If the airline books 71 people on a flight for which
the maximum number is 69, what is the probability that the number of
people who show up will exceed the capacity of the plane?

A) 0.005

B) 0.004

C) 0.001

D) 0.022

A) 0.005

Use binomcdf

trials = 71

P = .9

X = 69

= .995

1 - .995 = .005

A company purchases shipments of machine components and uses this
acceptance sampling plan: Randomly select and test 30 components and
accept the whole batch if there are fewer than 3 defectives. If a
particular shipment of thousands of components actually has a 6% rate
of defects, what is the probability that this whole shipment will be
accepted?

A) 0.165

B) 0.576

C) 0.277

D) 0.732

D) 0.732

Use binomcdf

trials = 30

P = .06

X = 2

A multiple choice test has 10 questions each of which has 5 possible
answers, only one of which is correct. If Judy, who forgot to study
for the test, guesses on all questions, what is the probability that
she will answer exactly 3 questions correctly?

A) 0.302

B) 0.799

C) 0.201

D) 0.00800

C) 0.201

Use binompdf

trials = 10

P = .2

X = 3

Suppose that 11% of people are left handed. If 5 people are selected
at random, what is the probability that exactly 2 of them are left
handed?

A) 0.0121

B) 0.0853

C) 0.0105

D) 0.171

B) 0.0853

Use binompdf

trials = 5

P = .11

X = 2

The probability is 0.6 that a person shopping at a certain store will
spend less than $20. For groups of size 24, find the mean number who
spend less than $20.

A) 8.0

B) 14.4

C) 12.0

D) 9.6

B) 14.4

24*.6

A company manufactures batteries in batches of 26 and there is a 3%
rate of defects. Find the mean number of defects per batch.

A) 7.8

B) 0.8

C) 78

D) 25.2

B) 0.8

26*.03

A company manufactures batteries in batches of 26 and there is a 3%
rate of defects. Find the standard deviation for the number of defects
per batch.

A) 0.6

B) 75.7

C) 0.8

D) 0.9

D) 0.9

sqrt of (26*.03*.97)

What is the probability that the random variable has a value greater
than 4?

A) 0.500

B) 0.375

C) 0.450

D) 0.625

A) 0.500

(8-4)*.125

What is the probability that the random variable has a value less
than 7.4?

A) 0.6750

B) 1.0500

C) 0.9250

D) 0.8000

C) 0.9250

7.4*.125

What is the probability that the random variable has a value between
0.1 and 6.2?

A) 0.8875

B) 0.7625

C) 1.0125

D) 0.6375

B) 0.7625

(6.2-.1)*.125

Find the area of the shaded region. The graph depicts the standard
normal distribution with mean 0 and standard deviation 1.

A) 0.8485

B) 0.1292

C) 0.8708

D) 0.8907

C) 0.8708

normalcdf upper = 1.13

Find the area of the shaded region. The graph depicts the standard
normal distribution with mean 0 and standard deviation 1.

A) 0.7224

B) 0.2224

C) 0.2776

D) 0.2190

C) 0.2776

normalcdf lower = .59

Find the area of the shaded region. The graph depicts the standard
normal distribution with mean 0 and standard deviation 1.

A) -0.0344

B) 0.0344

C) 0.4656

D) 0.9656

D) 0.9656

normalcdf lower = -1.82

If z is a standard normal variable, find the probability.

P(z > 0.59)

A) 0.7224

B) 0.2776

C) 0.2224

D) 0.2190

B) 0.2776

normalcdf lower = .59

If z is a standard normal variable, find the probability.

P(z < 0.97)

A) 0.8315

B) 0.8078

C) 0.8340

D) 0.1660

C) 0.8340

normalcdf upper = .59

If z is a standard normal variable, find the probability.

P(-0.73 < z < 2.27)

A) 1.54

B) 0.2211

C) 0.4884

D) 0.7557

D) 0.7557

normalcdf lower = -.73

normalcdf upper = 2.27

z0.05

A) 1.545

B) 1.755

C) 1.645

D) 1.325

C) 1.645

invNorm .05 no negative

Assume that adults have IQ scores that are normally distributed with
a mean of 100 and a standard deviation of 15 (as on theWechsler test).
Find the probability that a randomly selected adult has an IQ between
90 and 120 (somewhere in the range of normal to bright normal).

A) 0.6014

B) 0.6568

C) 0.6227

D) 0.6977

B) 0.6568

normalcdf lower = (90-100)/15

normalcdf upper = (120-100)/15

Find P40, which is the IQ score separating the bottom40% from the top
60%.

A) 96.1

B) 95.2

C) 95.6

D) 96.2

D) 96.2

15*(invnorm .4)+100

Find the IQ score separating the top 14% from the others.

A) 83.7

B) 104.7

C) 116.2

D) 99.8

C) 116.2

15*(invnorm 1-.14)+100

The amount of rainfall in January in a certain city is normally
distributed with a mean of 3.4 inches and a standard deviation of 0.3
inches. Find the value of the quartile Q1.

A) 0.9

B) 3.2

C) 3.6

D) 3.3

B) 3.2

.3*(invnorm .25)+3.4

Assume that women have heights that are normally distributed with a
mean of 63.6 inches and a standard deviation of 2.5 inches. Find the
value of the quartile Q3.

A) 66.1 inches

B) 67.8 inches

C) 64.3 inches

D) 65.3 inches

D) 65.3 inches

2.5*(invnorm .75)+63.6

Assume that X has a normal distribution, and find the indicated
probability.

The mean is μ = 137.0 and the standard deviation is σ = 5.3.

Find the probability that X is between 134.4 and 140.1.

A) 0.4069

B) 0.6242

C) 0.8138

D) 1.0311

A) 0.4069

normalcdf

lower = (134.4-137)/5.3 = -.49057

upper =
(140.1-137)/5.3 = .58491

=.4088 ????

The diameters of pencils produced by a certain machine are normally
distributed with a mean of 0.30 inches and a standard deviation of
0.01 inches.What is the probability that the diameter of a randomly
selected pencil will be less than 0.285 inches?

A) 0.0596

B) 0.4332

C) 0.0668

D) 0.9332

C) 0.0668

z = (.285-.3)/.01 = -1.5

normalcdf upper = -1.5

A bank's loan officer rates applicants for credit. The ratings are
normally distributed with a mean of 200 and a standard deviation of
50. If an applicant is randomly selected, find the probability of a
rating that is between 200 and 275.

A) 0.5

B) 0.4332

C) 0.9332

D) 0.0668

B) 0.4332

normalcdf

lower = (200-200)/50 = 0

upper =
(275-200)/50 = 1.5

The lengths of human pregnancies are normally distributed with a mean
of 268 days and a standard deviation of 15 days. What is the
probability that a pregnancy lasts at least 300 days?

A) 0.4834

B) 0.0166

C) 0.9834

D) 0.0179

B) 0.0166

normalcdf

lower = (300-268)/15 = 2.13

The scores on a certain test are normally distributed with a mean
score of 60 and a standard deviation of 2.What is the probability that
a sample of 90 students will have a mean score of at least 60.2108?

A) 0.1587

B) 0.3174

C) 0.8413

D) 0.3413

A) 0.1587

sqrt of 90 = 9.486832981

2 (stan dev)/9.486832981 =
0.210818511

new stan dev = 0.210818511

normalcdf

lower = (60.2108 - 60)/.210818511 = .999912196

Assume that women's heights are normally distributed with a mean of
63.6 inches and a standard deviation of 2.5 inches. If 90 women are
randomly selected, find the probability that they have a mean height
between 62.9 inches and 64.0 inches.

A) 0.0424

B) 0.1739

C) 0.7248

D) 0.9318

D) 0.9318

sqrt of 90 = 9.486832981

2.5 (stan dev)/9.486832981 =
0.2635231383

new stan dev = .2635231383

normalcdf

lower = (62.9 - 63.6)/.2635231383 = -2.66

lower = (64 - 63.6)/.2635231383 = 1.52

Suppose that replacement times for washing machines are normally
distributed with a mean of 9.3 years and a standard deviation of 1.1
years. Find the probability that 70 randomly selected washing machines
will have a mean replacement time less than 9.1 years.

A) 0.4286

B) 0.0714

C) 0.4357

D) 0.0643

D) 0.0643

sqrt 70 = 8.3666

1.1(stan dev)/8.3666 = .13148

new
stan dev = .13148

normalcdf

upper = (9.1 - 9.3)/.13148 = -1.5212

= .0641

A final exam in Math 160 has a mean of 73 with standard deviation
7.8. If 24 students are randomly selected, find the probability that
the mean of their test scores is greater than 78.

A) 0.0008

B) 0.8962

C) 0.0036

D) 0.0103

A) 0.0008

sqrt 24 = 4.89898

7.8(stan dev)/4.89898

new stan dev
= 1.59217

normalcdf

lower = (78 - 73)/1.59217 = 3.14037

= .0008

A final exam in Math 160 has a mean of 73 with standard deviation
7.8. If 24 students are randomly selected, find the probability that
the mean of their test scores is less than 76.

A) 0.0301

B) 0.9699

C) 0.8962

D) 0.9203

B) 0.9699

sqrt 24 = 4.89898

7.8(stan dev)/4.89898

new stan dev
= 1.59217

normalcdf

upper = (76 - 73)/1.59217 = 1.88422

=.9702

The given values are discrete. Use the continuity correction and
describe the region of the normal distribution that corresponds to the
indicated probability.

The probability of at least 42 boys

A) The area to the right of 42.5

B) The area to the right
of 42

C) The area to the right of 41.5

D) The area to the
left of 41.5

C) The area to the right of 41.5

at least = right -.5

The given values are discrete. Use the continuity correction and
describe the region of the normal distribution that corresponds to the
indicated probability.

The probability that the number of correct answers is between 22
and 48 inclusive

A) The area between 22.5 and 47.5

B) The area between 22
and 48

C) The area between 21.5 and 48.5

D) The area
between 21.5 and 47.5

C) The area between 21.5 and 48.5

between = -.5 & +.5

Estimate the indicated probability by using the normal distribution
as an approximation to the binomial distribution.

A certain question on a test is answered correctly by 22% of the
respondents. Estimate the probability that among the next 150
responses there will be at most 40 correct answers.

A) 0.0694

B) 0.1003

C) 0.8997

D) 0.9306

D) 0.9306

Use binomcdf

trials = 150

P = .22

X = 40

= .9278?

Estimate the indicated probability by using the normal distribution
as an approximation to the binomial distribution.

Two percent of hair dryers produced in a certain plant are
defective. Estimate the probability that of 10,000 randomly selected
hair dryers, exactly 225 are defective.

A) 0.0057

B) 0.0034

C) 0.0051

D) 0.0065

A) 0.0057

Use binompdf

trials = 10000

P = .02

X = 225

.0058?

Estimate the indicated probability by using the normal distribution
as an approximation to the binomial distribution.

Two percent of hair dryers produced in a certain plant are
defective. Estimate the probability that of 10,000 randomly selected
hair dryers, at least 219 are defective.

A) 0.0934

B) 0.9066

C) 0.0823

D) 0.0869

A) 0.0934

Use binomcdf

trials = 10000

P = .02

X = 218

1-.9055

.0945?