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velikii
12 days ago
6

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 .
Mathematics
1 answer:
Zina [12.3K]12 days ago
3 0

Response:

0.5; 0.34458

Detailed explanation:

Given the following:

Mean (m) = 28

Standard deviation, s = 5

To calculate the Z-score:

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)

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