Question

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)


= 8; = 6
P(5 ≤ x ≤ 17) =

Answer 1

Using the normal distribution, it is found that P(5 ≤ x ≤ 17) = 0.6247.

Normal Probability Distribution

In a normal distribution with mean $\mu$ and standard deviation $\sigma$, the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

• It measures how many standard deviations the measure is from the mean.

• After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem, we are given that $\mu = 8, \sigma = 6$.

The probability is the p-value of Z when X = 17 subtracted by the p-value of Z when X = 5, hence:

X = 17:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{17 - 8}{6}$

$Z = 1.5$

$Z = 1.5$ has a p-value of 0.9332.

X = 5:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5 - 8}{6}$

$Z = -0.5$

$Z = -0.5$ has a p-value of 0.3085.

0.9332 - 0.3085 = 0.6247.

Hence, P(5 ≤ x ≤ 17) = 0.6247.

More can be learned about the normal distribution at https://brainly.com/question/12517818