Question

Cindy is often late for work. Assume that the number of minutes that she is late for work follows a normal distribution with a mean of 20 minutes and a standard deviation of 9 minutes. Given that today is a sunny day, what is the probability that she will be between 16 and 28 minutes late for work tomorrow? round answer to four decimal places

Answer 1

Solution :

Given that ,

mean = = 20

standard deviation = = 9

P(16 < x < 28) = P[(16 - 20)/ 9) < (x - ) /  < (28 - 20) / 9) ]

= P(-0.44 < z < 0.88)

= P(z < 0.88) - P(z < -0.44)

= 0.8106 - 0.33

= 0.4806

probability = 0.4806