Question

The times of all 15 year olds who run a certain race are approximately normally distributed with a given mean Mu = 18 sec and standard deviation Sigma = 1. 2 sec. What percentage of the runners have times less than 14. 4 sec? 0. 15% 0. 30% 0. 60% 2. 50%.

Answer 1

The percentage of runners having times less than 14.4 sec is 0.15%. Then the correct option is A.

What is normal a distribution?

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

The times of all 15-year-olds who run a certain race are approximately normally distributed with a given mean (μ) = 18 sec and standard deviation (σ) = 1.2 sec.

The runners have times less than 14.4 sec.

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

$\rm z-score = \dfrac{X - \mu}{\sigma }\\\\z-score = \dfrac{14.4- 18}{1.2}\\\\z-score = -3$

Then the Percentage will be

$\rm P(X < 14.4) = P(z < -3) = 0.0013499 = 0.13499\ \% \approx 0.15\ \%$

More about the normal distribution link is given below.

brainly.com/question/12421652