(A)There are a hundred students in the class. We take an exam and it follows a n

Question

(A)There are a hundred students in the class. We take an exam and it follows a normal distribution with a mean of 78 and a standard deviation of 4. How many students to score between 74 and 82?
(B) We run a one sample T Test to test a sample of cars gas mileage against the population parameter of 22 miles per gallon. The standard error of the mean is 1.2 and our sample had a mean of 25 miles per gallon. What would b the T statistic?
(C) We run a correlation analysis in obtain a coefficient are of .25. How much of the variance does one variable explain in the other variable?

Explanation / Answer

a) P(74<X<82)=P((74-78)/4<Z<(82-78)/4)=P(-1<Z<1)=0.8413-0.1587=0.6827

b)here test stat =(X-mean)/std error =(25-22)/1.2=2.5

c) here coefficient of determination =r2 =0.252 =0.0625

hence 6.25% of the variance does one variable explain in the other variable

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