Question

question 5
1 pts
given a normal distribution with mean of 50 and a standard deviation of 4, what is the probability that
x<42?
o 0.9772
o 0.0228
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Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{X-\mu}{\sigma}\), where \(\mu = 50\), \(\sigma=4\), and \(X = 42\).

$$z=\frac{42 - 50}{4}=\frac{-8}{4}=- 2$$

Step2: Find the probability using the standard normal distribution table

We want to find \(P(X < 42)\), which is equivalent to \(P(Z<-2)\) (since \(z=-2\) from step 1).
Looking up \(z = - 2\) in the standard normal distribution table (the cumulative distribution function for the standard normal distribution \(\varPhi(z)\)), we know that \(P(Z < - 2)=0.0228\)

Answer:

\(0.0228\)