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Approximate normal distribution for a large group

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Children's gross motor development is assessed with an overall motor quotient, MQ, which was found to follow an approximate normal distribution for a large group of school children, with mean 93 and standard deviation 15.

a. What are the mean and standard deviation of sample mean MQ for a random sample of 144 children? b. What are the mean and standard deviation of sample mean MQ for a random sample of 36 children? c. In general, what values of sample mean MQ will result in a standardized sample mean (z) that is positive?

d. A sample of 144 children who participated in both club sports and regular sports had a mean MQ of 96.5. Report the z-score for this sample mean and use it to explain whether or not these children appear to be representative of the larger group in terms of MQ.

e. A sample of 36 obese children had a mean MQ of 85.7. Report the z-score for this sample mean and use it to explain whether or not these children appear to be representative of the larger group in terms of MQ.

Reference no: EM131817522

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