Question

question 6
given a normal distribution with mean of 50 and a standard deviation of 4, what is the probability that
x>43?
0.9599
-1.75
0.0401

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{X-\mu}{\sigma}\), where \(\mu = 50\), \(\sigma=4\), and \(X = 43\).

$$z=\frac{43 - 50}{4}=\frac{-7}{4}=-1.75$$

Step2: Find the probability using the standard normal distribution

We want to find \(P(X>43)\), which is equivalent to \(P(Z>-1.75)\) in the standard normal distribution (\(Z\)).
Since \(P(Z > z)=1 - P(Z\leq z)\), and from the standard normal table, \(P(Z\leq - 1.75)=0.0401\).

$$P(Z>-1.75)=1 - 0.0401 = 0.9599$$

Answer:

0.9599