1. The mean life of a battery is 50 hours with a standard deviation of 6 hours. The mean life of batteries follow a normal distribution. The manufacturer advertises that they will replace all batteries that last less than 38 hours. If 100,000 batteries were produced, how many would they expect to replace? In your answer explain your workings.
2. A quality contorl process uses a grading scale to grade the quality of the batteries. 1000 batteries are produced. It is assumed that the scores are normally distributed with a mean score of 75 and a standard deviation of 15 a) How many batteries will have scores between 45 and 75? b) If 60 is the lowest passing score, how many batteries are expected to pass the quality control check? In your answer, explain your workings.
3. The length of time the batteries are on the supermarket shelf before being solved is a mean of 12 days and a standard deviation of 3 days. It can be assumed that the number of days on the shelf follows a normal distribution. Answer the following questions, explai your workings for each.
a) About what percent of the batteries remain on the shelf between 9 and 15 days?
b) About what percent of the batteries remain on the shelf last between 12 and 15 days?
c) About what percent of the batteries remain on the shelf last 6 days or less?
d) About what percent of the batteries remain on the shelf last 15 or more days?
4. An online shopping store maintains the shopping history of users so that future predictions can be made about which products will appeal to which type of customer.
The following baskets are noted.
Calculate the Support and the Confidence, that a potential customer who adds A, and B to their shopping basket is likely to add product C. In your answer, explain your workings.
5. Which data algorithm would you choose for the following scenarios. In your answer please explain your choice, as to why it is the most appropriate, in brief how the algorithm works, and what the expected outcomes would be.
(a) the battery company you work for is considering opening a new manufacturing plant in Europe and has come down to the two last choices – Ireland or Poland. You have data such as the utility costs, employment rates, mean salary for the location, and grants available for the Government, such as the IDA. Which algorithm would you use to help you choose?
(b) the software company you work for monitors users’ online time, access to the SaaS, number of purchases, length of time online, the number of sessions, etc. They are interested in predicting which users are likely to be retained and which are likely to churn. What algorithm would help provide an insight to this problem?
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