Answer:
Z = -2.054 and Z = 2.054
Step-by-step explanation:
Z-score:
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.
Middle 96%
The normal distribution is symmetric, so:
From the: 50 - (96/2) = 2nd percentile
To the: 50 + (96/2) = 98th percentile
2nd percentile:
Z with a pvalue of 0.02. So Z = -2.054.
98th percentile:
Z with a pvalue of 0.98. So Z = 2.054.
Z = -2.054 and Z = 2.054
