IQ scores of UIU professors are normally distributed with a mean of 105 and a standard deviation of 21. In a random sample of 90, approximately how many Profs will have IQs between 84 and 133?
It should be absolutely routine. I don't know what else can be said about it. The answer, correct to four decimal places, is 0.7501.
I don't know how you've been taught to calculate normal probabilities so I can't suggest how you should get that answer.
The volume of questions you're posting will make it difficult, if not impossible, for you to get timely help. You're swamping the forum with questions and solutions you want answered and checked. Further, it's difficult to follow a lot of the work you're posting. Replies will probably trickle in over the fullness of time.
I get the feeling many of these are assignment questions that contribute to your course grade - if they are you're skating on thin ice with amount of help your asking ...... I apologise in advance if this is not the case.