a. What is the mean number of sales? b. What is the standard deviation of number of sales? c. Complete the table below.

Question

1.      The probability that a person buys a car from a particular dealership after a test-drive is 25%. From a sample of 100 people that took a test-drive,

a.      What is the mean number of sales?

b.     What is the standard deviation of number of sales?

c.      Complete the table below.

Number of sales	Probability of this number of success
21 to 29 sales
17 to 33 sales
At least 30 sales
At most 20 sales

Answer 1

n = 100 p = 0.25 q = 0.75 mean = np standard deviation (SD) = sqrt(npq)

x = number of sales

z = (x - mean)/SD =

P(21 <= x <= 29) = P(20.5 < x < 29.5) (continuity correction since approximating discrete binomial distribution with continuous normal distribution)

convert limits of inequality to z-stat:

P(20.5 < x < 29,.5) = P((20.5 - mean)/SD < z < (29.5 - mean)/SD))

determine probability using standard normal probability table lookup or utility on calculator

For other problems follow same process

P(17 <= x + 33) = P(16.5 < x < 33.5)

P(x >= 30) = P(x > 29.5)

P(x <= 20) = P(x < 20.5)