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Chapter 12: Problem 1

The scores on a test are normally distributed with a mean of 100 and a standard deviation of 20. In Exercises 1-10, find the score that is 1 standard deviation above the mean.

Short Answer

Expert verified
The score that is 1 standard deviation above the mean is 120.

Step by step solution

01

Understanding Normal Distribution

In a normal distribution, the mean, median and mode are the same. The distribution is symmetric about the mean, which means half of the values are to the left of center and other half to the right. Standard deviation tells us how measurements for a group are spread out from the average (or mean), or expected value.
02

Calculating Score

The assignment asks to find out what score is one standard deviation above the mean. To calculate the score that is 1 standard deviation above the mean we have to add 1 standard deviation value to the mean. In our case, the standard deviation is 20. Therefore, the score that is 1 standard deviation above the mean is \( Mean + 1 \times Standard \; deviation = 100 + 1 \times 20 = 120 \)

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Most popular questions from this chapter

A set of data items is normally distributed with a mean of 60 and a standard deviation of 8.Convert each data item to a z-score. 52

A set of data items is normally distributed with a mean of 400 and a standard deviation of 50. Find the data item in this distribution that corresponds to the given z-score. \(z=2.5\)

The data sets give the ages of the first six U.S. presidents and the last six U.S. presidents (through Barack Obama). AGE OF FIRST SIX U.S. PRESIDENTS AT INAUGURATION $$ \begin{array}{|l|c|} \hline \text { President } & \text { Age } \\ \hline \text { Washington } & 57 \\ \hline \text { J. Adams } & 61 \\ \hline \text { Jefferson } & 57 \\ \hline \text { Madison } & 57 \\ \hline \text { Monroe } & 58 \\ \hline \text { J. Q. Adams } & 57 \\ \hline \end{array} $$ AGE OF LAST SIX U.S. PRESIDENTS AT INAUGURATION $$ \begin{array}{|l|c|} \hline \text { President } & \text { Age } \\ \hline \text { Carter } & 52 \\ \hline \text { Reagan } & 69 \\ \hline \text { G. H. W. Bush } & 64 \\ \hline \text { Clinton } & 46 \\ \hline \text { G. W. Bush } & 54 \\ \hline \text { Obama } & 47 \\ \hline \end{array} $$ a. Without calculating, which set has the greater standard deviation? Explain your answer. b. Verify your conjecture from part (b) by calculating the standard deviation for each data set. Round answers to two decimal places.

A set of data items is normally distributed with a mean of 60 and a standard deviation of 8.Convert each data item to a z-score. 84

A set of data items is normally distributed with a mean of 60 and a standard deviation of 8.Convert each data item to a z-score. 74
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