A normal distribution has a mean of 137 and a standard deviation of 7. Find the z-score for a data value of 121. Incorrect Round to two decimal places g

The z-score for a data value of 121 is -2.29.

Step-by-step explanation:

In a set with mean and standard deviation , the zscore of a measure X is given by:

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.

In this problem, we have that:

Find the z-score for a data value of 121.

This is Z when X = 121. So

The z-score for a data value of 121 is -2.29.

.

Step-by-step explanation:

We have been given that a normal distribution has a mean of 137 and a standard deviation of 7. We are asked to find the z-score corresponding to data value 121.

We will use z-score formula to solve our given problem.

, where,

z = Z-score,

x = Sample score,

= Mean,

= Standard deviation.

Upon substituting our given values in above formula, we will get:

Upon rounding to two decimal places, we will get:

Therefore, z-score corresponding to data value 121 would be .

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