In a large population of adults, the mean IQ is 123 with a standard deviation of 17.

Question

In a large population of adults, the mean IQ is 123 with a standard deviation of 17. Suppose 60 adults are randomly selected for a market research campaign. (Round to 2 decimal places for all z-values and round all other answers to 4 decimal places, if needed.)

(a) The distribution of IQ is (b1)

(b) The distribution of the sample mean IQ is (b2) with a mean of _____ and a standard deviation of ______.

(c) The probability that the sample mean IQ is less than 120 is ______.

(d) The probability that the sample mean IQ is greater than 120 is _______.

(e) The probability that the sample mean IQ is between 120 and 128 is ______.

(b1) options: approximately normal/exactly normal/may or may not be normal/certainly skewed

(b2) options: approximately normal/exactly normal/not normal/skewed left/skewed right

Answer 1

Hi Mish L.,

You've asked 7 questions, in great detail, on the same skill set, all at the same time, without evidence you've even thought about the problems? That's spamming. Doing your entire problem set for you is first, forbidden under Wyzant rules, and second, won't help you acquire the skills you need. Ask one question, digest the lesson, and do the rest yourself -- that would be appropriate.

-- Cheers, --Mr. d.

Answer 2

First question - what is the distribution in this particular subset? (multiple choice from approximately normal; exactly normal; may or may not be normal ; certainly skewed)

Since IQ tests are purposely normalized with a mean of 100 and a sd of 15, the large sub population mentioned here represent the upper 6% or so of the full population. This would make the distribution within this sub group highly right skewed and not normal.

The remaining questions can not be answered with the information given as they are referring to a non normal distribution.