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.

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

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

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

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

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

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.

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

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

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