n 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

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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