Question

Find z z such that the proportion of observations that are less than z z in a standard normal distribution is 0.29 . 0.29. (Enter your answer rounded to two decimal places.)z= __.

Answer 1

z = -0.55.

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.

Find z z such that the proportion of observations that are less than z z in a standard normal distribution is 0.29 .

This is the value of Z that has a pvalue of 0.29.

So it is z = -0.55.