Question

Consider a large clothing shop in Sydney. Suppose it is known that the number of business suits sold per day is normally distributed with a mean, μ = 22 and standard deviation, σ = 10.  Mr Wood is employed to sell business suits. The number of business suits he sells each day for 35 days is recorded and the mean number per day calculated.

What is the probability that Mr Wood's average daily sales will be more than 26 business suits?  (4 dp)   Answer

Answer 1

Let x be the number of business suits sold per day

Given : mean ( µ ) = 22 and standard deviation (σ) = 10 and n = 35

According to sampling distribution of sample mean ( ).

The sample mean approximately follows normal distribution with mean = and standard deviation =

Therfore = 22 and   = = 1.6903

We are asked to find P( >26)

=

= P( z > 2.37 )

=1 - P( z ≤ 2.37 )

=1 - 0.9911 ----( from z score table , value corresponding to  z =2.37)

= 0.0089

Probability that Mr Wood's average daily sales will be more than 26 business suits is 0.0089