Question

A survey reveals that Z-score for a particular problem is -0.50. Assuming the distribution is normal, what is the value of the random variable x if the problem had a mean of 35 and a standard deviation of 10?

Answer 1

`X = 30`

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 = (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:

`Z = -0.5, \mu = 35, \sigma = 10`

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

`-0.5 = (X - 35)/(10)`

`X - 35 = -0.5*10`

`X = 30`