Answer to Question #327161 in Statistics and Probability for cosette

Question

A continuous random variable X is normally distributed with a mean of 45 and a standard deviation of 6. Illustrate a normal curve and find the probability of the following:

25-28 (4pts).  P(39 < X < 51)

29-32 (4pts).  P(33 < X < 63)

33-36 (4pts).  P(X > 45)

Answer 1

Normal curve

$P(39<X<51)=P(X<51)-P(X<39)=F({\frac {51-45} 6})-F({\frac {39-45} 6})=F(1)-F(-1)=2F(1)-1=2*0.84134-1=0.68268$

$P(33<X<63)=P(X<63)-P(X<33)=F({\frac {63-45} 6})-F({\frac {33-45} 6})=F(3)-F(-2)=0.99865-0.02275=0.9759$

45 is the mean, so P(X>45) = 0.5