Answer to Question #318713 in Statistics and Probability for eris

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

$(a) P(X < 52)=P(z < \frac{52-60}{8})\\=P(z < -1)=0.5-P(0<z < 1)\\=0.5-0.3413=0.1587 \\(b) P(48 < X < 64)=P(\frac{48-60}{8}<z < \frac{64-60}{8})\\=P(-1.5<z < 0.5)\\=P(0<z < 0.5)+P(0<z < 1.5)\\=0.1915+0.4332=0.6247 \\(c) P(X > 57)=P(z > \frac{57-60}{8})\\=P(z >-0.38)=0.5+P(0<z <0.38)\\=0.5+0.1480=0.6480$