Question

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.
(a) Write down the probability that the runner completed the race in more than 28 minutes. [1]
(b) Calculate the probability that the runner completed the race in less than 26 minutes. [2]
It is known that 20 % of the runners took more than 28 minutes and less than k minutes to complete the race.
(c) Find the value of k.

Answer 1

Answer:

Transcribed image text: 7. 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 points) b. Calculate the probability that the runner completed the race in less than 24 minutes c. It is known that 30% of the runners took more than 28 minutes and less than k minutes to complete the race. Find the value of k

Answer 2

The answer is 0.5 and 0.34458 respectively.

Given:

Mean = 28 minutes

Standard derivation = 5 minutes

To Find:

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

The probability that the runner completed the race in less than 26 minutes

Solution:

We can simply solve this problem by using the following mathematical process.

The formula of calculating Zscore

Zscore= (raw score - mean) ÷ standard derivation

If the race is completed in more than 28 minutes

Z score= $\frac{28-28}{5}$

Z score = 0

From the Zscore table, the probability is 0.5.

We subtract the probability from 1 for the probability of more than 28 minutes.

Probability (raw score is more than 28 minutes) = 1 - 0.5

Probability = 0.5

If the race is completed in less than 26 minutes

Zscore= $\frac{26-28}{5}$

Zscore = -0.4

Therefore, from the Zscore table, the probability is 0.34458

Hence, the answer is 0.5 and 0.34458 respectively.

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