Question

Answer the question for a normal random variable x with mean μ and standard deviation σ specified below. (Round your answer to one decimal place.) μ = 38 and σ = 11. Find a value of x that has area 0.01 to its right

Answer 1

Answer:

x = 63.6

Step-by-step explanation:

Problems of normally distributed samples are 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 and also the area to its left. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X, which is the area to its right.

In this problem, we have that:

$\mu = 38, \sigma = 11$

Find a value of x that has area 0.01 to its right

This is x when Z has a pvalue of 1-0.01 = 0.99. So it is X when Z = 2.3267.

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

$2.3267 = \frac{X - 38}{11}$

$X - 38 = 11*2.3267$

$X = 63.6$

So x = 63.6