Question

question 21 of 28
suppose a normal distribution has a mean of 50 and a standard deviation of 3. what is ( p(x leq 44) )?
a. 0.84
b. 0.16
c. 0.025
d. 0.975

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 44\), \(\mu=50\), and \(\sigma = 3\).

$$z=\frac{44 - 50}{3}=\frac{-6}{3}=- 2$$

Step2: Find the probability using the standard normal distribution table

We want to find \(P(X\leq44)\), which is equivalent to \(P(Z\leq - 2)\) in the standard normal distribution.
From the standard normal distribution table, \(P(Z\leq - 2)=0.0228\approx0.025\) (using the property that for a standard normal distribution \(Z\), \(P(Z\leq - z)=1 - P(Z\leq z)\) and \(P(Z\leq2)=0.9772\), so \(P(Z\leq - 2)=1 - 0.9772 = 0.0228\)).

Answer:

C. 0.025