Assume that X has a normal distribution, and find the indicated probability.
-The mean is $\mu = 15.2$ and the standard deviation is $\sigma = 0.9$. Find the probability that $X$ is greater than 17.
A)0.9713
B)0.9772
C)0.0228
D)0.9821

Question

Quizplus · Accepted Answer

To find the probability that $X$ is greater than 17, we first calculate the z-score using the formula $z = \frac{X - \mu}{\sigma}$, where $X = 17$, $\mu = 15.2$, and $\sigma = 0.9$. This gives us $z = \frac{17 - 15.2}{0.9} = 2$. Looking up the z-score of 2 in the standard normal distribution table, we find the area to the left of $z = 2$ is approximately 0.9772. Since we want the area to the right (the probability that $X$ is greater than 17), we subtract this from 1, giving $1 - 0.9772 = 0.0228$.

Assume That X Has a Normal Distribution, and Find the Indicated