Question

X is a normally distributed random variable with mean 52 and standard deviation 7.What is the probability that X is between 45 and 59?Use the 0.68-0.95-0.997 rule and write your answer as a decimal.

Answer 1

We know that

`\begin{gathered} \mu=52 \\ \sigma=7 \end{gathered}`

If X is a normally distributed random variable with mean 52 and standard desviation 7, the probability that X is between 45 and 59 is represented as

So,

`45=\mu-\sigma`

By a similar calculation

`59=\mu+\sigma`

This means

[tex]P(45taking into account that X is normally distributed and using the 0.68-0.95-0.997 rule[tex]P(\mu-\sigmaSo, P (45 < X < 59) = 0.68