Question

Find the diameter that represents the 49th percentile

Answer 1

Using the normal distribution, the diameter that represents the 49th percentile is of 1.52 units.

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.

Using a calculator, the mean and the standard deviation for the diameters are given as follows:

$\mu = 1.524, \sigma = 0.1226$

The 49th percentile is X when Z = -0.025, hence:

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

$-0.025 = \frac{X - 1.524}{0.1226}$

X - 1.524 = -0.025 x 0.1226

X = 1.52.

More can be learned about the normal distribution at brainly.com/question/15181104

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