Question

assume the random variable x is normally distributed with mean μ = 50 and standard deviation σ = 7. find the indicated probability. p(x > 38) p(x > 38)= (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, $x = 38$, $\mu=50$, and $\sigma = 7$. So, $z=\frac{38 - 50}{7}=\frac{- 12}{7}\approx - 1.7143$.

Step2: Find the probability using the standard normal table

We want $P(x>38)$, which is equivalent to $P(z>-1.7143)$ in the standard normal distribution. Since the total area under the standard - normal curve is 1, and $P(z > a)=1 - P(z\leq a)$. From the standard normal table, $P(z\leq - 1.7143)\approx0.0436$. So, $P(z>-1.7143)=1 - 0.0436 = 0.9564$.

Answer:

$0.9564$