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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- 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:
[tex]\mu = 1.524, \sigma = 0.1226[/tex]
The 49th percentile is X when Z = -0.025, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.025 = \frac{X - 1.524}{0.1226}[/tex]
X - 1.524 = -0.025 x 0.1226
X = 1.52.
More can be learned about the normal distribution at https://brainly.com/question/15181104
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