Question

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
Shaded area is 0.4013.

Answer 1

Answer:

Z = -0.25

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, which is also the shaded area under the normal table, 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.

In this problem:

The z-score is the value of Z which has a pvalue of 0.4013. Looking at the z-table, Z = -0.25

Answer 2

The z score that corresponds with an area of 0.4013 is -0.25

z score is used to determine by how many standard deviations the raw score is above or below the mean.

The z score is given by:

$z=\frac{x-\mu}{\sigma/ } \\\\where\ x\ is\ raw\ score,\mu\ is\ mean, \sigma\ is\ standard\ deviation$

Given that μ = 0, σ = 1, the shaded area is 0.4013

The z score that corresponds with an area of 0.4013 is -0.25

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