A researcher collects IQ data on a sample of individuals. The z-score for the sa

Question

A researcher collects IQ data on a sample of individuals. The z-score for the sample mean was +3.00. The researcher reports that their sample mean was 110 and the population is 100 with a standard deviation of 15. However they did not give the sample size. What was the researchers sample size?

In a normal distribution of exam scores, the average exam score is 75 with a standard deviation of 10. Which 2 exam scores mark the middle 50% of scores?

IQ test scores are standarized to produce a normal ditribution with a mean of 100 and a standard deviation of 15. What is the proportion of individuals that fall below an IQ score of 110?

Explanation / Answer

here for z=(X-mean)/std error

hence std error =(110-100)/3 =10/3

and std error =std deviation/(n)1/2

hence n1/2 =15/(10/3) =4.5

hence n=~20

2)for middle 50 lie at 25 and 75 percentile for which z=0.6745

hence corresponding score =mean +/- z*std deviation = 68.255 ; 81.745

3)P(X<110)=P(Z<(110-100)/15)=P(Z<0.6667)=0.7475

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