General Statistics: Ch 5 Test

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This course is designed to acquaint the student with the principles of descriptive and inferential statistics. Topics will include: types of data, frequency distributions and histograms, measures of central tendency, measures of variation, probability, probability distributions including binomial, normal probability and student's t distributions, standard scores, confidence intervals, hypothesis testing, correlation, and linear regression analysis. This course is open to any student interested in general statistics and it will include applications pertaining to students majoring in athletic training, pre-nursing and business.
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1

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied:

A police department reports that the probabilities that 0, 1, 2, 3, and 4 car thefts will be reported in a given day are 0.183, 0.311, 0.264, 0.150, and 0.064, respectively.

Not a probability distribution. The sum of the P(x)'s is not 1, since 0.9720 ≠ 1.000.

2

A company manufactures batteries in batches of 25 and there is a 3% rate of defects.

Find the standard deviation for the number of defects per batch.

0.9

3

A machine has 12 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail.

Find the probability that the machine will be working.

0.795

4

Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 1 or a 6, nothing otherwise.

What is your expected value?

-$1.33

5

A company manufactures batteries in batches of 18 and there is a 3% rate of defects.

Find the mean number of defects per batch.

0.5

6

The brand name of a certain chain of coffee shops has a 54% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a coffee shop in the town. He selects a random sample of 10 Coffleton residents.

Find the probability that exactly 4 of the 10 Coffleton residents recognize the brand name.

0.169

7

The Acme Candy Company claims that 8% of the jawbreakers it produces actually result in a broken jaw. Suppose 9571 persons are selected at random from those who have eaten a jawbreaker produced at Acme Candy Company.

Would it be unusual for this sample of 9571 to contain 797 persons with broken jaws?

No, 797 people are within 2 standard deviations of the mean.

8

Determine whether the following is a random variable, and if it is, whether it is discrete or continuous:

The number of pixels in a digital photo.

Discrete

9

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 0.5470, 0.3562, 0.0870, 0.0094, and 0.0004, respectively. Round answer to the nearest hundredth.

µ = 0.56

10

The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.4521, 0.3970, 0.1307, 0.0191, and 0.0010, respectively.

Find the standard deviation for the probability distribution.

σ = 0.77