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# Normal Approximation to Binomial

1. You attempt a 50 item (n = 50) true-and-false exam. You did not study for the material and your attempt to answer any item is a guess, with a 50% chance that you will get any item correct. You need a score of 30 or better to pass the exam.

A. If you are truly guessing your way through the exam, what is the probability that you will answer any item incorrect?
B. What is the average number of items you can expect to guess correctly?
C. What is the probability you will pass the exam by merely guessing on each item?
D. What is the probability you will get a C, i.e., the probability you will get 35 or more correct?

2. Assume that the average adult height in North America for anyone over the age of 18 is 68 inches, with a standard deviation of 3.50 inches.

A. What is the probability that someone selected randomly from the adult population in North America is less than 64 inches tall?
B. What is the probability that someone selected randomly from the adult population in North America is more than 71 inches tall?
C. What is the probability that someone selected randomly from the adult population in North American is more than 64 inches tall but less that 71 inches tall?