Answer to Question #326838 in Statistics and Probability for Cath

Question

2. 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

ve score 50?

b. below score 38?

a.

3.

Consider the normal distribution of IQs with a mean of 100 and a standard dev

Answer 1

$P(X>50)=1-P(X<50)=1-P(Z<\frac{x-\mu}{\sigma})=1-P(Z<\frac{50-45}{4})=1-(Z<1.25)=1-0.89435=0.10565$

b. $P(X<38)=P(Z<\frac{x-\mu}{\sigma})=P(Z<\frac{38-45}{4})=P(Z<-1.75)=0.04006$