Provide an Appropriate Response $\underline { \text { Student's solution: } }$

question 57

Essay

Provide an appropriate response.
-A variable is normally distributed with a mean of 100 and a standard deviation of 10. A student wanted to find the percentage of observations of the variable lying between 106 and 110. What is wrong with his solution?
$\underline { \text { Student's solution: } }$ $\mathrm { z }$ -scores: $\frac { 106 - 100 } { 10 } = 0.6 \quad \frac { 110 - 100 } { 10 } = 1.0$ Percentage of scores lying between 106 and 110 $\begin{array} { l } = \text { difference between } z \text {-scores } \\ = 1.0 - 0.6 = 0.4 = 40 \% \end{array}$

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