Question

question 2 of 10
suppose a normal distribution has a mean of 266 and a standard deviation of 12. what is ( p(xgeq278) )?
a. 0.16
b. 0.475
c. 0.84
d. 0.975

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 266\), \(\sigma=12\), and \(x = 278\).

$$z=\frac{278 - 266}{12}=\frac{12}{12}=1$$

Step2: Use the standard normal distribution table

We know that \(P(X\geq x)=P(Z\geq z)\). For a standard normal distribution \(Z\), \(P(Z\geq1)=1 - P(Z < 1)\).
From the standard normal distribution table, \(P(Z < 1)=0.8413\approx0.84\). So \(P(Z\geq1)=1 - 0.84 = 0.16\)

Answer:

A. 0.16