Question

Find the probability of selecting a z score between -0.85 and 1.15

Answer 1

Answer:

67.72% probability of selecting a z score between -0.85 and 1.15

Step-by-step explanation:

Z - score

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.

Find the probability of selecting a z score between -0.85 and 1.15

This is the pvalue of Z = 1.15 subtracted by the pvalue of Z = -0.85

Z = 1.15 has a pvalue of 0.8749

Z = -0.85 has a pvalue of 0.1977

0.8749 - 0.1977 = 0.6772

67.72% probability of selecting a z score between -0.85 and 1.15

Answer 2

Answer:

0.6772

Step-by-step explanation:

Use a z-score table.

P(-0.85 < z < 1.15) = P(z < 1.15) − P(z < -0.85)

P(-0.85 < z < 1.15) = 0.8749 − 0.1977

P(-0.85 < z < 1.15) = 0.6772