IQ score is normally distributed with a mean of 100 and a s.d. of 15.
a. The probability that a randomly selected person has an IQ score lower than 72
b. The probability that a selected person has an IQ score between 130 and 150
c. Tom is among the lower 15% of the population in term of IQ score. What are the possible IQ scores that he has
d. If a random sample of 64 people is selected, find the probability that the sample mean is higher than 107. How likely is it to draw such a sample
probability question
2008-01-26 11:28 pm
回答 (1)
2008-01-26 11:41 pm
✔ 最佳答案
Let X be the IQ score(a)
Pr(X<72)
=Pr(Z<(72-100)/15)
=Pr(Z<-1.8667)
=0.030972
(b)
Pr(130<X<150)
=Pr((130-100)/15<Z<(150-100)/15)
=Pr(2<Z<10/3)
=0.02232
(c)
Pr(Z<Y)=0.15
Y=-1.0364
So X=100-(1.0364)(15)=84.454
The possible IQ scores that he has is less than 84.454
(d)
Pr(X>107)
=Pr(Z>8(107-100)/15) [because standard deviation=15/8]
=Pr(Z>3.7333)
=0.000094
The possibility to draw such a sample is very low !
收錄日期: 2021-04-25 16:58:32
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