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In: Statistics and Probability

IQ scores are scaled to have a mean of 100 and a standard deviation of 15....

IQ scores are scaled to have a mean of 100 and a standard deviation of 15. They are also supposed to follow a normal distribution. Suppose a random sample of 81 people are given IQ tests. Calculate the probability that the sample mean IQ is greater than 102.

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Expert Solution

Solution :

Given that ,

mean = = 100

standard deviation = = 15

n = 81

= 100

=  / n = 15/ 81=1.6667

P( >102 ) =1 - P( < 102)

=1- P[( - ) / < (102-100) /1.6667 ]

= 1-P(z <1.20 )

Using z table  

= 1- 0.8849   

probability=0.1151

orchestra answered 2 years ago
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