Question

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.) = 8; = 2 P(7 ≤ x ≤ 11)

Answer 1

Using the normal distribution, the indicated probability is given as follows:

P(7 ≤ x ≤ 11) = 0.6247.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

• The z-score measures how many standard deviations the measure is above or below the mean.

• Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

$\mu = 8, \sigma = 2$

P(7 ≤ x ≤ 11) is the p-value of Z when X = 11 subtracted by the p-value of Z when X = 7, hence:

X = 11:

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

Z = (11 - 8)/2

Z = 1.5

Z = 1.5 has a p-value of 0.9332.

X = 7:

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

Z = (7- 8)/2

Z = -0.5

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

0.9332 - 0.3085 = 0.6247.

More can be learned about the normal distribution at brainly.com/question/28096232

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