Question

Four friends, Janice, Barbara, Kathy and Roberta, decided to carpool together to get to school. Each day the driver would be chosen randomly selecting one of the four names. they carpool to school for 92 days. use the normal approximation to the binomial to calculate the following probabilities. round the standard deviation to four decimal places. (round your answer to four decimal places.)

a) find the probability that Janice is the driver at most 19 days.

Answer 1

Answer:

Given,

sample n = 92

p = 1/4 = 0.25

Mean = np

= 92*0.25

= 23

Standard deviation = sqrt(npq)

substitute values

= sqrt(0.25*0.75*92)

= 4.1533

a)

P(X < 19.5) = P((x-u)/s < (19.5 - 23)/4.1533)

= P(z < -0.84)

= 0.2004542 [since from z table]

= 0.2005