Problem
Question 9, 7.2.RA-1 HW Score: $16.67 \%, 2.5$ of 15 points Part 1 of 3 Points: 0 of 1 Save 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) Ask my instructor Clear all Check answer
Solution
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 \(\boxed{-1.27}\).
