I have 7 statistics (probability) problems. All the details in the attached excel. It must be done using Excel and in details. Please reply back only if you are really sure that you can solve them. Please don’t waste your and my time:

1. A venture capital firm is evaluating the performance of a possible high tech investment. Bill Buce, a senior partner, has suggested using a continuous uniform distribution to model net income. Bill believes the net income for year one will vary between -2.18 and 12.2 (in millions).

What net income should Bill forecast if he wants to be 75% sure net income will not exceed his forecast? Forecasted net income =

2. An automated bottling machine fills 20oz bottles of diet coke. The actual fill volume varies according to a uniform distribution between 18.5 oz and 19.2 oz. What is the probability that a bottle chosen at random will contain more than 19.19 oz?

3. During peak hours on a busy Friday evening, a patient arrives at a local hospital’s emergency room, on average, every 0.043 minutes (believed to follow an exponential distribution). What is the probability that the next patient will arrive in more than 0.0579 minutes?

4. Mike Mochado is the head barrista at John’s Java & Jerk, a local cafe serving coffee, cold beverages, and food items with a Carribbean flair. Mike’s big concern at the moment is deciding how many pounds of coffee beans he’ll need for the week. The guy from corporate told Mike to assume that coffee bean usage is normally distributed. On the basis of the cafe’s first 20 weeks of operation, Mike has determined that his average weekly coffee bean usage is 165.5 pounds, with a standard deviation of 46.34 pounds.

How many pounds of coffee beans should Mike have on hand to be 82.6 % sure that he’ll have enough beans?

5. Allen Allenby runs the hot dog concession at the local high school’s football games and is responsible for forecasting the number of hot dogs they’ll need on any given Friday night. Allen believes that hot dog demand follows a normal distribution with mean 113.75 and standard deviation 11.38.

What is the probability that on any Friday evening, demand for hot dogs will exceed 94.3 hot dogs?

Pr{ X > 94.3 } =

6. A cashier at the Hungry Bear Restaurant in Disneyland’s Critter Country serves an average of 25.25 customers per hour (believed to follow a Poisson distribution). Always conscious of managing park guests’ waiting line experience, the disney operations research team wants to post a sign telling customers about the restaurant’s efficiency. If the manager wants to be 94 % sure she doesn’t overestimate, what time should she list?

Time (in minutes) per order =

7. This one has a drawn table and it is available in the attached excel sheet under (prob7).

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