Statistics (probability) | Mathematics homework help

 

Statistics (probability)

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Requested to be solved using excel please. A total of 11 problems, 3 have drawings and sent as attachement:

 

1.     On average, a car arrives at a local Starbucks drive through every 1.07 minutes. The process is believed to follow a Poisson distribution. What is the probability that exactly 33 cars arrive in 1.25 hour(s)?

 

2.     If the probability of a defective light bulb is 0.06, to be 98 % confident, up to how many defective lightbulbs should you expect in a sample of 40 lightbulbs?

 

3.     A quality engineer at Intel is responsible for testing chips before they are shipped to Intel’s customers. Historical data indicates that chips are defective with probability 0.03. The engineer randomly selects 19 chips from a large production batch. What is the probability the engineer will find exactly 6 defective chips?

 

4.     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 40 days of the new program, the manager determined that 5 % of customers were not satisfied with the results of their call. If the manager checks a random sample of 33 calls, what is the probability that 1 or fewer customers will be dissatisfied with the results of their call?

 

5.     On average, Jimbo’s Luxury Resort receives 6.3 reservation calls every hour (assumed to follow a Poisson distribution). What is the probability that no more than 1 calls are received in 1.25 hour(s)?

 

6.     A hot dog concession at Safeco Field sells an average of 33.2 hot dogs per hour (believed to follow a Poisson Distribution). How many hot dogs should the vendor stock in order to be 93% sure it has enough hot dogs for 2.5 hour(s)?

 

7.     Two TVs are randomly selected from a large shipment. Each has a 0.03 probability of being defective. Calculate Pr{ 1st good and 2nd defective }.

 

8.     Happy Harry’s Hamburgers recently commissioned a top tier consulting company to develop a new location selection process. However, after receiving the first invoice from the consulting company, Happy Harry wasn’t… happy that is, and he decided to cancel the remainder of the engagement. Along with the invoice, the consulting company provided Happy Harry with the results of their study to date. The company had analyzed Happy Harry’s previous location selections, categorizing them as huge successes, successes, or failures. Here is what they reported: 

 77.19 % of past locations were a success 

 17 % of past locations were a failure 

 Happy Harry was underwhelmed by this information. However, the company also applied a model it developed to Harry’s past hugely successful, successful, and failed locations. Given a huge success, the model predicted success 93.5 % of the time. Given a success, the model predicted success 92.5 % of the time. Given a failure, the model predicted failure 77.5 % of the time. 

 Now what Happy Harry really wants to know is the probability of a success given a predicted success. So, give Harry a helping hand and calculate Pr{S|PS}:

 

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