Step 6
(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between \$35 and
\$39?
If we assume the x distribution is approximately normal, we will convert the x values in the given interval P(35 ? x ? 39) to z
scores, but instead of using the standard error $\sigma_x$, we can use the standard deviation of x, $\sigma = 9$. Use the standard deviation and
the given mean $\mu = 37$ to calculate the z score corresponding to x = 35, rounding the result to two decimal places.
$z = \frac{x - \mu}{\sigma}$
$\frac{35 - 37}{9}$
$0.2$
Calculate the z-score corresponding to x = 39, rounding the result to two decimal places.
$z = \frac{x - \mu}{\sigma}$
$\frac{39 - 37}{9}$
$0.2$
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