IQs of Individuals Are Normally Distributed with a Mean of 100

question 24

Essay

IQs of individuals are normally distributed with a mean of 100 and a standard deviation of 16. If you sampled students at your college and assumed, as the null hypothesis, that they had the same IQ as the population, then in a random sample of size
(a)n = 25, find Pr( $\bar { Y }$ < 105).
(b)n = 100, find Pr( $\bar { Y }$ > 97).
(c)n = 144, find Pr(101 < $\bar { Y }$ < 103).

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Definitions:

Standard Deviation

A measure of the amount of variation or dispersion of a set of values, indicating how spread out the values are from the mean.

Standard Deviation

A measure of the dispersion or variability within a set of numerical data, indicating how spread out the numbers are.

Standardize

To make consistent by conforming to a set standard or protocol to ensure uniformity and comparability.

IQ Test

A standardized test designed to measure human intelligence and cognitive abilities in relation to an average population.