Question

It has been found that times taken by people to complete a particular tax form follow a normal distribution with mean 100 minutes and standard deviation 30 minutes.

(a) Four people are chosen at random. What is the probability that exactly two of them take longer than an hour to complete this form?

(b) For a randomly chosen person, state in which of the following ranges (expressed in minutes) time to complete the form is least likely to lie.

70-90 90-110 110-130 130-150

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	100
std deviation   =σ=	30.0000

P(a student take longer than an hour to complete this forum:

probability =

P(X>60)

=

P(Z>-1.333)=

1-P(Z<-1.33)=

1-0.0918=

0.9082

hence P(exactly 2 out of 4 will take longer than 1 hour to complete)=⁴C₂(0.9082)²(0.0918)² =0.0417

b)as range 130-150 falls at the maximum distance , therefore it is least likely to lie in range 130-150