Question

The heights of horses who compete in the Melbourne Derby are normally distributed with a mean of 66 inches and a standard deviation of 3 inches (a) If a horse is randomly selected from this race, what height would you expect it to be? (b) What percentage of horses who compete in the Melbourne Derby have heights between 60 and 72 inches? (c) In a particular year there are 25 horses running in the Melbourne Derby. How many of these would you expect to have a height of less than 63 inches?

Answer 1

Kindly check explanation

Explanation:

Given that:

Distribution = Normal

Mean(m) = 66

Standard deviation (σ) = 3 inches

A.) If horse is randomly selected from the race, Expected height = mean of the distribution = 66

B.) % horses with height between 60 and 72

Using the relation :

X = 60 ; 72

Z = (x - mean) σ

Z = (60 - 66) / 3

Z = - 6/3

Z = - 2

P(Z < - 2) = 0.0228 (using table)

Z = (72 - 66) / 3

Z = 6/3

Z = 2

P(Z < 2) = 0.9772 (using table)

P(score being between 60 and 72):

0.9772 - 0.0228= 0.9544

C) number of samples = 25

Height less than 63 inches :