Question

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.

Answer 1

a)

for normal distribution z score =(X- $\mu$ )/ $\sigma$
here mean=       $\mu$ =	120
std deviation   = $\sigma$ =	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