1. It is reported that the distribution of peoples IQ measured by a popular IQ test has the mean of 100 and standard deviation of 15. Given this information, what is the probability of randomly sampling a person who score

(a)100 or higher?

(b)Higher than 115?

(c)Between 85 and 115?

2. Given the information in question #1, between what two scores can the probability of randomly sampling a person become 95%? (Hint: The z-scores corresponding to this probability are + 1.96)

3. You set a criterion that if you randomly sample someone with IQ that falls into the extreme 5% of the population, this is considered to be an extreme score. If you sample someone whose IQ is 130, can you conclude that this is an extreme score (given the same population mean and standard deviation as presented in Question #1)?

Please show step by step as I am having difficulty in understanding these questions.