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
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:
The variance of the distribution is 0.132.
The probability of success remains the same from trial to trial.
The mean or expected value for a binomial probability distribution is μ = nπ.
To apply a Poisson probability distribution, the mean can be computed as μ.
16. David's gasoline station offers 4 cents off per gallon if the customer pays in cash...
1. Sponsors of a local charity decided to attract wealthy patrons to its $500-a-plate dinner by allowing each patron to buy a set of 20 tickets for the gaming tables. The chance of winning a prize for each of the 20 plays is 50–50. If you bought 20 tickets, what is the chance of winning 15 or more prizes? Multiple Choice 0.006 0.250 0.750 0.021 3. An insurance agent has appointments with four prospective clients tomorrow. From past experience the...
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 45% of all customers pay in cash. During a one-hour period twenty-five customers buy gasoline at this station. What is the probability that at least nine pay in cash?
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 more than 8 and less than 12 customers pay in cash?