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 .
1 answer:
Answer:
0.5 ; 0.34458
Step-by-step 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)
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