Question

X is a normally distributed random variable with a mean of 60 and standard

deviation of 8. Find the probabilities indicated by using the table.

(a) P(X < 52)

(b) P(48 < X < 64)

(c) P(X > 57)

Answer 1

a. $P(X<52)=P(X<\frac{x-\mu}{\sigma})=P(X<\frac{52-60}{8})=P(X<-1)$

P(X<52)=0.1581

b.

$P(48<X<64)=P(\frac{48-64}{8}<X<\frac{64-60}{8})=P(-1.5<X<0.5)=0.1915+0.4332=0.6247$

c. $P(X>57)=P(X>\frac{57-60}{8})=P(X>-0.375)=1-P(X<-0.375)=1-0.35569=0.64431$