Question

A normal distribution has a mean of 15 and a standard deviation of 2. Find the value that corresponds to the 75th percentile.

Answer 1

Answer:

The value that corresponds to the 75th percentile is 16.35.

Step-by-step explanation:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

A normal distribution has a mean of 15 and a standard deviation of 2.

This means that $\mu = 15, \sigma = 2$

Find the value that corresponds to the 75th percentile.

This is X when Z has a pvalue of 0.75. So X when $Z = 0.675$

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

$0.675 = \frac{X - 15}{2}$

$X - 15 = 2*0.675$

$X = 2*0.675 + 15$

$X = 16.35$

The value that corresponds to the 75th percentile is 16.35.