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

Answer:

$X = 30$

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. 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:

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

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

$-0.5 = \frac{X - 35}{10}$

$X - 35 = -0.5*10$

$X = 30$