PIQ (Pritchard’s Intelligent Quotient) scores are normally distributed with a mean of 120 and a standard deviation of 10.4.
a. What is the probability that a person selected at random has a PIQ score greater than 135?
b. What is the probability that an individual has a PIQ score between 104 and 126?
c. The gifted program at Centereach High School accepts students with a PIQ score in the top 10% of the population. What PIQ score would a student need to have to be accepted to the program?
d. Find the PIQ score at the 55th percentile.
a)
for normal distribution z score =(X-)/ | |
here mean= = | 120 |
std deviation == | 10.400 |
probability that a person selected at random has a PIQ score greater than 135:
probability = | P(X>135) | = | P(Z>1.44)= | 1-P(Z<1.44)= | 1-0.9251= | 0.0749 |
b)
probability that an individual has a PIQ score between 104 and 126:
probability = | P(104<X<126) | = | P(-1.54<Z<0.58)= | 0.7190-0.0618= | 0.6572 |
c)
for highest 10 percentile ; critical z =1.28
hence corresponding score =mean +z*std deviation =120+1.28*10.4= 133.3~ 134
d)
for 55th percentile ; critical z =0.13
hence corresponding score =mean +z*std deviation =120+0.13*10.4= 121.35
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