Question

Mean = 25

Standard Deviation = 3.8


P(X

Find the value of k.


Round to 2 decimal values.

Answer 1

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

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 = (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 = (X - \mu)/(\sigma)`

`Z = (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.