Question

Time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 8 min and standard deviation 3 min. if five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (round your answer to four decimal places.)

Answer 1

Given:

z = (x - μ)/σ = z value
x = independent variable = 11
μ = mean = 8
σ = standard deviation = 3

Solution:

X ~ N (8, 3)

For day 1, n = 5

P (X < = 11) = P (Z < = 11 – 8 / 3/Sqrt5) = P (Z < =2.23) = 0.987126

For day 1, n = 6

P (X < = 11) = P (Z < = 11 – 8 / 3/sqrt6) = P (Z < =2.45) = 0.992857

For both days:

P (X <= 11) = P (X <= 11) = (0.987126) (0.992857) = 0.9801