statistics - normal distribution multiple choice

Question

 

The variable X is normally distributed with a mean u and a standard deviation o. Let A be a value of X. For the current values of u, o, and A it is known that P(X<A)=.4512. If the value of of the mean u and the value of A remain fixed, reducing the value of o will result in what?

 

A.) P(X<A) increase

 

B.) P(X<A) decrease

 

C.) P(X<A) remain the same?

 

 

Answer 1

Since the Normal Distribution is symmetric, P(X<A)=0.4512 tells us that A < u. If r=u-A, then the central interval around u of radius r is (u-r,u+r)=(A,2u-A). This region's probability will increase when you decrease o, since the bounds become more standard deviations from the mean. This also means that the tails (-∞,A] and [2u-A,∞), which both match each other in probability, have their probability decrease. Thus the correct choice is (B).