Answer to Question #303624 in Statistics and Probability for ash

Question

In a Math test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability that a score picked at random will lie below 45

Answer 1

Since $\mu$ =45 and $\sigma$=4 we have:

P(X<45) = P(X-$\mu$ < 45-45) = P($\frac{x-\mu}\sigma$ < $\frac{45-45}{4}$)

Since

Z = $\frac{x-\mu}{\sigma}$ = $\frac{45-45}{4}$ = 0

Then

P(X<45) = P(Z<0)

From the normal distribution table, we find that:

P(Z<0) = 0.5

Therefore, we conclude that the probability that a score picked at random will lie below 45 is 0.5