Question

IQ tests are standardized and follow a normal distribution. On a common IQ test, the mean score is 100 with a standard deviation of 15.

a) What is the probability that a randomly selected individual gets a score of 105 or higher?

b) What are the mean and standard deviation of the average score of an SRS of 50 people? (Don't forget to justify this)

c) What is the probability that the average score of an SRS of 50 people is 105 or higher?

Answer 1

@WolframWizard This should be my last question!!

For b, I'm pretty sure the mean is 150, and you use the formula to get the standard deviation.

Answer 2

For a, do I just convert to a z score?

Answer 3

and then use a normal table to find the probability?

Answer 4

I'm not sure if I divide by the sample size here to find the z score, though.

Answer 5

sorry, I meant the SD ^^

Answer 6

FOR PART b: MEAN IS 100 sorry xD

Answer 7

wow

Answer 8

a) use the normalcdf function on your calculator. It will be bounded at 105 as the lowest and ∞ at the highest. Just use any really high number for ∞ if you don't have a calculator with CAS. Plug in the mean and SD to get normlafcdf(105,high number,100,15) and this is equal to .369. Converting to a z-score would work as well

b) I think what you have is correct.

c) Just plug what you get from b) into the same function as a) or convert to z-score

Answer 9

what would be p, in finding the SD?