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Function and Probability

1. A new book is being released and a bookstore predicts that 70% of customers that walk through the door on the release day will purchase the book. If 30 customers walk through the door, answer the following: (MUST SHOW WORK)
A) What type of distribution function (name) is the model for this situation?
B) What is the expected number of requests for the new book (based on the 30 customers)?
C) What is the variance?
D) What is the probability that at most 20 people will want the book?
E) How many copies of the book should the bookstore have on hand, if the store wants the probability of not having enough books to satisfy the demand to be less than 5%?

2. The national population distribution of scores on a high school graduation equivalency test is normal with a mean of 75 and a standard deviation of 12 (on a scale of 1 to 100).
A) If a student is randomly selected, what is the probability this his score is less than 69?
B) If a sample of 16 students are taken from this distribution what is the probability that the mean of the sample will be less than 69?

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