Question

assume the random variable x is normally distributed with mean μ = 50 and standard deviation σ = 7. find the indicated probability. p(x > 42) p(x > 42) = (round to four decimal places as needed.)

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$. Here, $x = 42$, $\mu=50$, and $\sigma = 7$. So, $z=\frac{42 - 50}{7}=\frac{-8}{7}\approx - 1.1429$.

Step2: Use the standard normal distribution

We want to find $P(x>42)$, which is equivalent to $P(z>-1.1429)$ in the standard normal distribution. Since the total area under the standard - normal curve is 1, and $P(z > a)=1 - P(z\leq a)$. Looking up $P(z\leq - 1.1429)$ in the standard normal table, we find $P(z\leq - 1.1429)\approx0.1271$. Then $P(z>-1.1429)=1 - 0.1271 = 0.8729$.

Answer:

$0.8729$