__Business Statistics I (STAT 220)__

__Question 1:__

Use Excel to generate the probability distribution for a binomial random variable for which there are 20 trials (n = 20) and the probability of success is 0.5 (p = 0.5), and show the graph.

__Question 2:__

Dan is not a good student. His exam strategy is to rely on luck for the next quiz. The quiz consists of 25 questions. Each question has four possible answers, only one of which is correct. Dan plans to guess the answer to each question. Answer the following questions:

- Using the Binomial Formula, find the probability that Dan gets exactly 8 answers correct?
- What is the probability that Dan gets more than 8 (X > 8) answers correct?
- What is the expected value of the number of correct answers? What is the variance of the number of correct answers?

__Question 3:__

The random variable x is known to be uniformly distributed between 10 and 20.

- Compute P(x ≤ 18).
- Compute P(13 ≤ x ≤ 16).
- Compute P(x=17).

__Question 4__

Scores of high school students on a national calculus exam were normally distributed with a mean of 86 and a standard deviation of 4. (Total possible points = 100.)

- What is the probability that a randomly selected student will have a score more than 80?
- What is the probability that a randomly selected student will have a score less than 90?
- What is the probability that a randomly selected student will have a score between 80 and 90?

__Question 5__

According to the Sleep Foundation, the average night’s sleep is 6.8 hours. Assume the standard deviation is 0.6 hours and that the probability distribution is normal.

- What is the probability that a randomly selected person sleeps more than 8 hours?
- What is the probability that a randomly selected person sleeps 6 hours or less?
- Doctors suggest getting between 7 and 9 hours of sleep each night. What percentage of the population gets this much sleep?

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