Posted: December 23rd, 2022

1. The call center manager at InsuranceCorp is responsible for ensuring customer satisfaction. To this end, she recently implemented a new rating program. At the conclusion of each call, the customer is transferred to an automated survey attendant and asked to indicate whether he was satisfied or disatisfied with the call.

During the first 49 days of the new program, the manager determined that 2 % of customers were not satisfied with the results of their call. If the manager checks a random sample of 46 calls, what is the probability that 3 or fewer customers will be dissatisfied with the results of their call?

Hint: Be very careful when entering answers smaller than 0.0001.

2. 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 153.75 pounds, with a standard deviation of 49.2 pounds.

How many pounds of coffee beans should Mike have on hand to be 76.3 % sure that he’ll have enough beans?

3. A hot dog concession at Safeco Field sells an average of 17 hot dogs per hour (believed to follow a Poisson Distribution). How many hot dogs should the vendor stock in order to be 90% sure it has enough hot dogs for 3 hour(s)?

4. 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 333 and standard deviation 169.83.

What is the probability that on any Friday evening, demand for hot dogs will not exceed 654 hot dogs?

Hint: Be very careful when entering answers smaller than 0.0001.

Pr{ X <= 654 } =

5. On average, Jimbo’s Luxury Resort receives 6.2 reservation calls every hour (assumed to follow a Poisson distribution). What is the probability that more than 2 calls are received in 1.5 hour(s)?

Hint: Be very careful when entering answers smaller than 0.0001.

Pr{ X > 2 } =

6. A cashier at the Hungry Bear Restaurant in Disneyland’s Critter Country serves an average of 36 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 87 % sure she doesn’t underestimate, what time should she list?

Time per order =

7. An automated bottling machine fills 20oz bottles of diet coke. The actual fill volume varies according to a uniform distribution between 19.37 oz and 20.01 oz. What is the probability that a bottle chosen at random will contain no more than 19.48 oz?

Hint: Be very careful when entering answers smaller than 0.0001.

Pr{ X <= 19.48 } =

8. 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 -1.58 and 17.32 (in millions).

What net income should Bill forecast if he wants to be 76% sure net income will not exceed his forecast?

Forecasted net income =

9. On average, a car arrives at a local Starbucks drive through every 0.41 minutes. The process is believed to follow a Poisson distribution. What is the probability that exactly 12 cars arrive in 0.5 hour(s)?

Hint: Be very careful when entering answers smaller than 0.0001.

10. During peak hours on a busy Friday evening, a patient arrives at a local hospital’s emergency room, on average, every 0.0325 minutes (believed to follow an exponential distribution). What is the probability that the next patient will arrive in more than 0.0177 minutes?

Hint: Be very careful when entering answers smaller than 0.0001.

Pr{ T > 0.0177 } =

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