Answer to Question #175818 in Statistics and Probability for Janna

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 38

Answer 1

X ~ N(45, 4²)

$P(X<38) = P(\frac{x-μ}{σ} < \frac{38-45}{4}) \\ = P(Z < -1.75) \\ = 0.040 \\ = 4.0 \%$