Question

Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph. Assume the variable x is normally distributed.

SAT Critical Reading Scores 200 < x < 375Score μ=501 σ=115 A graph titled S A T Critical Reading Scores has a normal curve over a horizontal x-axis labeled Score from less than 200 to more than 800. Vertical line segments extend from the horizontal axis to the curve at 200 and 375, where 375 is to the left of center. The area under the curve between 200 and 375 is shaded and labeled 200 less than x less than 375. The equations mu equals 501 and sigma equals 115 are displayed on the graph.The probability that the member selected at random is from the shaded area of the graph is

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	501
std deviation   =σ=	115.000

probability =P(200<X<375)=P((200-501)/115)<Z<(375-501)/115)=P(-2.62<Z<-1.1)=0.1357-0.0044=0.1313