Answer to Question #24627 in Statistics and Probability for Ellie

Question #24627
The mean IQ score for 1500 students is 100, with a standard deviation of 15. Assuming the scores have a normal curve, a. how many have an IQ between 85 and 115? b. how many have an IQ between 70 and 130? c. how many have an IQ over 145?
1
Expert's answer
2013-02-25T11:53:21-0500
a. how many have an IQ between 85 and 115?
z(115) = (115-100)/15 = 1
z(85) = (85-100)/15 = -1
We need to consult Z-table to find P value with this Z value
P(85< x < 115) = P(-1< z < 1) = 0.6827
Quantity of people of 1500 that have IQ between 85 and 115 = 0.6827*1500 ~ 1024

b. how many have an IQ between 70 and 130?
z(115) = (130-100)/15 = 2
z(85) = (70-100)/15 = -2
P(-2< z < 2) = 0.6827
# of 1500 that have IQ between 70 and 130 = 0.6827*1500 ~ 1024

c. how many have an IQ over 145?
Z(>145)=( 145-100)/15=3

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