Question

Suppose a normal distribution has a mean of 50 and a standard deviation of3. What is P(x≤44)?OA. 0.975OB. 0.84OC. 0.16OD. 0.025

Answer 1

Step-by-step explanation:

Given:

mean = 50

standard deviation = 3

distribution is a normal distribution

To find:

P(x≤44)

To determine the probability, we will apply the z-score formula:

`\begin{gathered} \begin{equation*} z=(X-μ)/(σ) \end{equation*} \\ \mu\text{ = mean} \\ \sigma\text{ = standard devation} \\ X\text{ = value} \end{gathered}`
`\begin{gathered} z\text{ = }\frac{44\text{ - 50}}{3} \\ \\ z\text{ = }(-6)/(3) \\ \\ z\text{ = -2} \end{gathered}`

Next, we will find P(z ≤ -2):