Question

The playing time X of classical CDs has the normal distribution with mean 54 and standard

Answer 1

Using the normal distribution, it is found that the relative frequency of classical CDs with playing time X between 49 and 69 minutes is 0.8403 = 84.03%.

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:

$\mu = 54, \sigma = 5$

The relative frequency of classical CDs with playing time X between 49 and 69 minutes is the p-value of Z when X = 69 subtracted by the p-value of Z when X = 49, hence:

X = 69:

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

$Z = \frac{69 - 54}{5}$

Z = 3

Z = 3 has a p-value of 0.9987.

X = 49:

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

$Z = \frac{49 - 54}{5}$

Z = -1

Z = -1 has a p-value of 0.1584.

0.9987 - 0.1584 = 0.8403.

More can be learned about the normal distribution at brainly.com/question/4079902

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