Assist with 4 question HW

1. A local bar keeps records of Happy Hour (5:00 P.M. to 6:00 PM), number of customers arriving. On average, 10 customers arriving during the happy hour. Let's assume these arrivals follow the Poisson distribution. On a given day, what is probability of at most 7 customers will arrive during the Happy Hour?

2. Your business plan indicates that the new product line may turn in $55,000 profit next year if demand is strong, $35,000 profit if demand is average and $18,000 loss if demand is weak. Market study shows 25% probability for a strong demand, 40% probability for average demand, and 35% for a weak demand next year. What is the expected monetary value (EMV) of this new product line for next year?

3. A management professor gives a quiz containing 15 True/False questions. Past data suggests the probability to be 0.78 that a student chooses the correct answer for any given question. What is the probability that a student selected at random will answer at least 13 questions correctly? Assume binomial distribution applies.

4. The probability that an article in Big Brand magazine has a typographical error is 0.05. The next edition has 18 articles. What is the probability that the magazine (all 18 articles) will have exactly one typographical error? Assume binomial distribution.