the times of all 15 year olds who run a certain race are approximately normally distributed with a given…

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. what percentage of the runners have times less than 14.4 sec? 0.15% 0.30% 0.60% 2.50%

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. what percentage of the runners have times less than 14.4 sec? 0.15% 0.30% 0.60% 2.50%

Answer

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 14.4$, $\mu=18$, and $\sigma = 1.2$. $z=\frac{14.4 - 18}{1.2}=\frac{- 3.6}{1.2}=-3$

Step2: Use the standard normal distribution table

The standard - normal distribution table gives the cumulative probability $P(Z\lt z)$. Looking up $z=-3$ in the standard normal distribution table, we find that $P(Z\lt - 3)=0.00135\approx0.15%$

Answer:

0.15%