Question

The Malthouse Charity Run is a 5 kilometre race. The time taken for each runner to complete the race was recorded. The data was found to be normally distributed with a mean time

of 28 minutes and a standard deviation of 5 minutes.

A runner who completed the race is chosen at random.

Write down the probability that the runner completed the race in more than 28 minutes.

3b. [2 marks]

Calculate the probability that the runner completed the race in less than 26 minutes.

3c. [3 marks]

It is known that 20% of the runners took more than 28 minutes and less than minutes to complete the race.

Find the value of .

Answer 1

0.5 ; 0.34458

Explanation:

Given that:

Mean (m) = 28

Standard deviation, s = 5

To obtain the Zscore :

Z = (x - m) / s

1.) P(x > 28)

Z = (28 - 28) / 5

Z = 0

P(Z > 0) = 0.5 (Z probability calculator)

2.) P(x < 26)

Z = (26 - 28) / 5

Z = - 0.4

P(Z > -0.4) = 0.34458 (Z probability calculator)