Question

Mean = 25

Answer 1

Answer:

The normal distribution is explained for the solution of this question.

Step-by-step explanation:

Normal Probability Distribution:

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.

Mean = 25, Standard Deviation = 3.8

This means that $\mu = 25, \sigma = 3.8$

So

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

$Z = \frac{X - 25}{3.8}$

If P(X > k) = a

We have to find $X = k$ when Z has a pvalue of 1 - a.

If P(X < k) = a

We have to find $X = k$ when Z has a pvalue of a.