Answer to Question #181319 in Statistics and Probability for Sophia Denise Melor

Question

Answer the question below

In a math test, the mean score is 45 and the standard deviation is 4. Assuming normality, what is the probability that the score will lie: 

If the score is above 58

If the score is below 49

If the score is below 68

If the score is above 55

If the score is above 38

Answer 1

$\mu = 45 \\ \sigma = 4 \\ P(X>58) = 1 -P(X<58) \\ = 1 -P(Z< \frac{58-45}{4}) \\ = 1 -P(Z<3.25) \\ = 1 -0.9994 \\ = 0.0006 \\ P(X<49) = P(Z< \frac{49-45}{4}) \\ = P(Z< 1) \\ = 0.8413 \\ P(X<68) = P(Z< \frac{68-45}{4}) \\ = P(Z< 5.75) \\ = 0.9999 \\ P(X>55) = 1 -P(X<55) \\ = 1 -P(Z< \frac{55-45}{4}) \\ = 1 -P(Z<2.5) \\ = 1 -0.9937 \\ = 0.0063 \\ P(X>38) = 1 -P(X<38) \\ = 1 -P(Z< \frac{38-45}{4}) \\ = 1 -P(Z< -1.75) \\ = 1 -0.04006 \\ = 0.95994$