IQs of Individuals Are Normally Distributed with a Mean of 100

question 6

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 $\operatorname { Pr } ( \bar { Y } < 105 )$ .
(b) $n = 100$ , find $\operatorname { Pr } ( \bar { Y } > 97 )$ .
(c) $n = 144$ , find $\operatorname { Pr } ( 101 < \bar { Y } < 103 )$ .

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Definitions:

Fed's Monetary Policy

The strategies employed by the Federal Reserve System to regulate the amount of money in circulation and influence interest rates to achieve economic objectives like controlling inflation or stimulating growth.

Federal Funds Rate

The interest rate at which banks lend reserve balances to other banks overnight, which is determined by the Federal Reserve in the U.S.

M1 Money Supply

A classification within the money supply encompassing all tangible forms of money such as currency and coins, alongside demand deposits and additional liquid assets owned by the central bank.

M2 Money Supply

A measure of the money supply that includes cash, checking deposits, and easily convertible near money, such as savings deposits and money market securities.