The Blacktop Speedway is a supplier of automotive parts. Included in stock are 7 speedometers that are correctly calibrated and two that are not. Three speedometers are randomly selected without replacement. Let the random variable z represent the number that are not correctly calibrated. Complete the probability distribution table. (Report probabilities accurate to 4 decimal places.)
x P(x)
0
1
2
3

x P(x)

0 0.4167

1 0.5

2 0.0833

3 0

Step-by-step explanation:

The speedometers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this question:

7 + 2 = 9 speedometers, which means that

2 are not correctly calibrated, which means that

3 are chosen, which means that

Complete the probability distribution table.

Probability of each outcome.

So

Only 2 defective, so

Probability distribution table:

x P(x)

0 0.4167

1 0.5

2 0.0833

3 0