Question

16. David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station. What is the probability that all 15 pay in cash?

Multiple Choice

• 0.0

• 0.9

• 0.1

• 1.0

17. For the following distribution:

x	P(x)
0	0.900
1	0.09
2	0.007
3	0.003

What is the variance of the distribution?

Multiple Choice

• 1.000

• 2.1

• 0.132

• 0.364

18. Which is true for a binomial distribution?

Multiple Choice

• The value of π is equal to 1.50.

• The probability of success remains the same from trial to trial.

• It approximates the Poisson distribution.

• There are 10 or more possible outcomes.

19. The mean or expected value for a binomial probability distribution is _________.

Multiple Choice

• μ = π(1 −π)

• μ = nπ

• μ = nπ(1 −π)

• μ = πn(1 −n)

22. To apply a Poisson probability distribution, the mean can be computed as __________.

Multiple Choice

• ∑ xn∑ xn

• nπ

• e −x

• μx e−μX !

25. Sweetwater & Associates write weekend trip insurance at a very nominal charge. Records show that the probability that a motorist will have an accident during the weekend and file a claim is 0.0005. Suppose they wrote 400 policies for the coming weekend, what is the probability that exactly two claims will be filed?

rev: 10_13_2017_QC_CS-105294, 10_23_2017_QC_CS-106063

Multiple Choice

• 0.8187

• 0.0164

• 0.0001

• 0.2500

Answer 1

Answer 2

16. The probability that all 15 customers pay in cash can be calculated using the binomial probability formula:

P(X = k) = (nCk) * p^k * (1 - p)^(n - k)

where n is the total number of customers (15), k is the number of customers paying in cash (15), and p is the probability that a customer pays in cash (0.40).

Plugging in the values:

P(X = 15) = (15C15) * (0.40)^15 * (1 - 0.40)^(15 - 15)

P(X = 15) = 1 * (0.40)^15 * (0.60)^0

P(X = 15) = (0.40)^15 * 1

P(X = 15) = 0.0000000000000064

Therefore, the probability that all 15 customers pay in cash is approximately 0.0000000000000064, which can be rounded to 0.0000.

The answer is 0.0%.

The answers to questions 17, 18, 19, and 22 are as follows:

17. The variance of the distribution is 0.132.

18. The probability of success remains the same from trial to trial.

19. The mean or expected value for a binomial probability distribution is μ = nπ.

20. To apply a Poisson probability distribution, the mean can be computed as μ.