Question

the variable x is normally distributed. the population mean is 15.2, and the population standard deviation is 0.900. find p(x > 16.1). round your answer to four decimal places.

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 16.1\), \(\mu=15.2\), and \(\sigma = 0.9\).

$$z=\frac{16.1 - 15.2}{0.9}=\frac{0.9}{0.9}=1$$

Step2: Find the probability using the standard normal distribution

We want to find \(P(X>16.1)\), which is equivalent to \(P(Z > 1)\) (since \(z = 1\) from Step1).
Using the property \(P(Z>z)=1 - P(Z\leq z)\). From the standard normal table, \(P(Z\leq1)=0.8413\).

$$P(Z > 1)=1-0.8413 = 0.1587$$

Answer:

\(0.1587\)