The stock price for International Business Machines (IBM) historically has followed an approximately normal distribution (when adjusting for inflation) with a mean of $166.305 and standard deviation of $4.2216. What is the probability that on a selected day the stock price is below $162.5?

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50.  If 64 applications are randomly selected, what is the probability that the mean credit rating of these 64 applicants will be between 205 and 275. (Round your answer to 4 decimal places.) (Calculator: http://statisticshelper.com/normal-distribution-calculator) A. 0.5011 B. 0.4113 C. 0.2119 D. 0.3664

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is $133,000. Assume the standard deviation is $45,000. Suppose you take a simple random sample of 22 graduates. Round all answers to four decimal places if necessary.   For a single randomly selected graduate, find the probability that her salary is between $136,209 and $142,906. For a simple random sample of 22 graduates, find the probability that the average salary is between $136,209 and $142,906. For part 2), is the assumption of normal necessary? No Yes

Cody took his first physics exam and scored an 80. The population mean for this exam is 70, and the standard deviation is 5. What is the probability of selecting a person with a score greater than Cody’s?