Question

In: Statistics and Probability

A worldwide organization of academics claims that the mean IQ score of its members is 115...

A worldwide organization of academics claims that the mean IQ score of its members is 115 , with a standard deviation of 17. A randomly selected group of 40 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 114.4. If the organization's claim is correct, what is the probability of having a sample mean of 114.4 or less for a random sample of this size? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Expert Solution

Solution:

We are given that: a worldwide organization of academics claims that the mean IQ score of its members is 115 , with a standard deviation of 17.

That is: Mean = and Standard Deviation =

Sample size= n = 40

Sample mean =

We have to find: the probability of having a sample mean of 114.4 or less for a random sample of this size.

That is find:

Find z score.

Thus we get:

Look in z table for z = -0.2 and 0.02 and find the corresponding area.

P( Z < -0.22 ) = 0.4129

Thus

Thus the probability of having a sample mean of 114.4 or less for a random sample of this size is 0.413

orchestra answered 2 years ago

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