Question 9, 7.2.RA-1
HW Score: $16.67 \%, 2.5$ of 15 points
Part 1 of 3
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Suppose $X$ is a normal random variable with mean $\mu=44$ and standard deviation $\sigma=11$
(a) Compute the $z$-value corresponding to $X=30$.
(b) Suppose the area under the standard normal curve to the left of the $z$-value found in part (a) is 0.1016 . What is the area under the normal curve to the left of $X=30$ ?
(c) What is the area under the normal curve to the right of $X=30$ ?
(a) $z=\square$
(Round to two decimal places as needed)
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Answer
So, the z-value corresponding to $X=30$ is \(\boxed{-1.27}\).
Step 1 ：Given that $X = 30$, $\mu = 44$, and $\sigma = 11$.
Step 2 ：We need to calculate the z-value, which is given by the formula $z = \frac{X - \mu}{\sigma}$.
Step 3 ：Substituting the given values into the formula, we get $z = \frac{30 - 44}{11}$.
Step 4 ：Solving the above expression, we get $z = -1.2727272727272727$.
Step 5 ：Rounding the z-value to two decimal places, we get $z = -1.27$.
Step 6 ：So, the z-value corresponding to $X=30$ is \(\boxed{-1.27}\).
