Question

The random variable X denotes the time taken for a computer link to be made between the terminal in an executive's office and the computer at a remote factory site. It is known that X has a Normal distribution with mean 15 seconds and standard deviation 3 seconds. P (X > 20) has value (choose the closest option).a. 0.048b. 0.052c. 0.098d. 0.786

Answer 1

a. 0.048

Explanation:

Problems of normally distributed samples 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.

In this problem, we have that:

`\mu = 15, \sigma = 3`

P(X > 20) is 1 subtracted by the pvalue of Z when X = 20. So

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

`Z = (20 - 15)/(3)`

`Z = 1.67`

`Z = 1.67` has a pvalue of 0.952.

So P(X>20) = 1 - 0.952 = 0.048.

The correct answer is:

a. 0.048