Question

Problem 4: (4 points) The time X taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with = 10 minutes and a = 2 minutes. (a) If five individuals fill out a form, what is the distribution of X, the average time taken by all five and find P(X <8). (2) (b) Suppose now that X is no longer normally distributed, but the mean and standard deviation are the same. However, 45 applicants fill the form. Answer the same questions as in (a). [2]

Answer 1

The solution to this problem is given by

Solution Given =10 X' denote the n=5 students Mina e=lo samble mean of XuNl4, 2 (Xunton J5 L P ( X 8) = P(X-Mił 8-10 9155 - PLZ <-2. 236) 0.012676 0.0197 distribution of the taken by tive students will be appleonimate nermal with Mił lo, tł=2 So, the avellere and P(x 28) 0.0127

b When "X' is no longer normal and same. meone and SD X' denote Students, Te let the average of n=45 with Then by Central limit theorem ix is normally distributed Mr == lo Un TĂ Ju 5 P(x <8) = P(X-Mał L 8-10 21545 - PlzL-6-708) JT . O =