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Chapter 12: Problem 33

A set of data items is normally distributed with a mean of 60 and a standard deviation of 8 . In Exercises 33-48, convert each data item to a z-score. 68

Short Answer

Expert verified
The z-score value of the data item 68 is 1.

Step by step solution

01

Identifying the known values

From the exercise, it is known that the mean (\(\mu\)) is 60, the standard deviation (\(\sigma\)) is 8, and the data item (\(X\)) is 68
02

Plugging the known values into the z-score formula

The next step is to substitute these known values into the z-score formula. So, we get: \(Z = \frac{{68 - 60}}{8}\).
03

Calculating the z-score

Calculate the fraction, which results in \(Z = 1\).

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Most popular questions from this chapter

Intelligence quotients (IQs) on the Stanford-Binet intelligence test are normally distributed with a mean of 100 and a standard deviation of 16. In Exercises 23-32, use the 68-95-99.7 Rule to find the percentage of people with IQs between 68 and 132 .

Two students have scores with the same percentile, but for different administrations of the SAT. Does this mean that the students have the same score on the SAT? Explain your answer.

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The scores on a test are normally distributed with a mean of 100 and a standard deviation of 20.Find the score that is \(2 \frac{1}{2}\) standard deviations above the mean.
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