Question

Find z such that 59% of the standard normal curve lies between −z and z. (Round your answer to two decimal places.)

Answer 1

Z = 0.82

Explanation:

When the distribution is normal, we use 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 such that 59% of the standard normal curve lies between −z and z.

The normal distribution is symmetric, which means that this is:

From the 50 - (59/2) = 20.5th percentile

To the 50 + (59/2) = 79.5th percentile.

The 20.5th percentile is -Z and the 79.5th percentile is Z.

79.5th percentile

Z with a pvalue of 0.795.

Looking at the z-table, it is Z = 0.824.

Rounding to two decial places, the answer is Z = 0.82.