The times of all 15 year olds who run a certain race are approximately normally distributed with a given mean mu = 18 sec and st

Question

2 years ago

9

andard deviation sigma = 1.2 sec. what percentage of the runners have times less than 14.4 sec?

1 answer:

Maru [420] · Answer 1 · 2023-03-23T09:53:47+03:00

The percentage of runners that have times less than 14.4 seconds that is P(x<14.4) is 0.0013499 which is approximately = 0.15%.

<h2>What is standard deviation?</h2>

The standard deviation of a data set is defined as how the data is dispersed in relation to the mean.

From the question,

The raw time given (X) = 14.4 sec

The mean value(m) = 18sec

The standard deviation(d) = 1.2 sec

Using the formula,

z = X - m/ d

z= 14.4- 18/1.2

z = -3.6/1.2

z= -3

Using a Z table to find the percentage equivalent of P(x<14.4) is 0.0013499 which is approximately = 0.15%.

Therefore, the percentage of runners that have times less than 14.4 seconds that is P(x<14.4) is 0.0013499 which is approximately = 0.15%.

Learn more about standard deviation here:

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