Midterm Exam ? Chapters 1 to 5. Each question is worth 10 points for a total of 100 points. 1. Historical data for a local steel manufacturing company shows that the average number of defects per standard sheet of steel is 2. In addition, the number of defects per unit is distributed according to Poisson distribution. A batch has just been completed. What is the probability that the first three units manufactured in this batch will contain at least a total of 4 defects? 2. X has the following probability distribution P(X): Compute the mean and variance of distribution. 3. For a binomial process, the probability of success is 40% and the number of trials is 5. Find P(X>4). 4. A test has 6 multiple choice questions, each with 4 alternatives. What is the probability of guessing 5 or more questions correctly? 5. The manager of the local grocery store has determined that, on the average, 4 customers use the service desk every half-hour. Assume that the number of customers using the service desk has a Poisson distribution. What is the probability that during a randomly selected half-hour period no more than 2 customers use the service desk? 6. An advertising campaign is being developed to promote a new bookstore opening in the newest mall development. To develop an appropriate mailing list it has been decided to purchase lists of credit card holders from MasterCard and American Express. Combining the lists they find the following: 40% of the people on the list have only a MasterCard and 10% have only an American Express card. Another 20% hold both MasterCard and American Express. Finally, 30% of those on the list have neither card. Given that a person has a MasterCard is the probability that person also has an American Express Card? 7. At a certain university, 30% of the students major in zoology. Of the students majoring in zoology, 60% are males. Of all the students at the university, 70% are males. What percentage of the students are males majoring in zoology? 8. In a normally distributed population, what tolerance interval contains a. 68.26 percent of all measurements? b. 95.44 percent of all measurements? 9. Determine the mean, median, and mode of the data set 95,86,78,90,62,73,89,92,84,76. 10. How many classes should be created for a frequency histogram containing: a. 130 values in a data set? b. 120 values in a data set?,If there is any way to show your work as much as possible so I could comprehend what's going on for future reference. Thank you!!,On question #2 I forgot to disclose the chart for the question; below it is provided. Thank you! X 1 2 3 4 P(X) .1 .5 .2 .2 Is 4pm today a reasonable time for you?
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