Answer :
Answer:
Z = 0.82
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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.