Question

An ice-cream producer’s sales are affected by the maximum daily temperature (typically, more sales when it is hotter). In summer the maximum daily temperature (in degrees Celsius) has a normal distribution with a mean of 31 and a variance of 25. The probability that the average maximum daily temperature on 18 randomly selected summer days is higher than 29 degrees is (to two decimal places)

Answer 1

Solution :

Given, X follows Normal distribution with,

   = 31

² = 25 , = 5

A sample of size n = 18 is taken from this population.

Let be the mean of sample.

The sampling distribution of the is approximately normal with

Mean = = 31

SD =      = 5/​18 = 1.17851130198  

Find P(X > 29)

= P[(X - )/ >  (29 - )/]

= P[Z > (29 - 31)/1.17851130198]

= P[Z > -1.70]

= 1 - P[Z < -1.70]

= 1 - 0.0446 ......... ( use z table)

= 0.9552 = 0.96