- The Department of Engineering at Stevens Institute of Technology conducted a study on the average number of trains passing through the Hoboken train station. The study showed that the average is six per hour and that the passing of these trains is approximated by the Poisson distribution.
(a) Find the probability that no trains passed through the Hoboken train station between 8am and 9.0am on Tuesday.
(b) Find the probability that exactly four trains passed during that time.
(c) Find the probability that exactly six trains passed during that time.
(d) Find the probability that ten or more trains passed during that time.
- Wegmans food stores conducted a study to see how many customers will return to the same store in the future. The study showed that 40% of the customers visiting a specific store will return in the future to the same store. Suppose seven customers are selected at random, what is the probability that:
(a) Exactly four customers will return?
(b) All seven customers will return?
(c) At least six customers will return?
(d) At least one customer will return?
(e) How many customers would be expected to return to the same store?
- Students taking Professor’s Angela Mazza’s Introduction to Marketing course spent an average of 1.5 hours to complete an assignment with a standard deviation of 0.40 hours and it follows the normal probability distribution.
(a) Find the portion of the students who spent between 1.5 and 2.5 hours to complete an assignment.
(b) Find the portion of the students who spent more than 2.5 hours to complete an assignment.
(c) Find the portion of the students who spent between 2.5 and 2.7 hours to complete an assignment.
(d) Find the portion of the students who spent between 1 and 2.7 hours to complete an assignment.
- The Coaches of the NJ Pride Women’s Soccer Club surveyed 144 of their players to see how much time they spend practicing on their own during the weekends. The study showed that the players practice an average of 20 hours on their own with a standard deviation of 9 hours.
(a) What is the standard error of the mean?
(b) Compute the probability the sample mean is greater than 20 hours?
(c) Compute the probability the sample mean is less than 18 hours?
(d) Compute the probability the sample mean is between 18 and 21 hours?
- Sears is in the process of hiring a new Manager for its Monmouth Mall store and they are trying to estimate the best annual healthcare premium. In a sample of 30 Managers, they found that the average yearly premium needed is $16,469 with a standard deviation of $2,000.
(a) What is the population mean? What is the best estimate of the population mean?
(b) Develop an 95% confidence interval for the population mean.
(c) Assuming a 99% level of confidence, how large of a sample is required with an acceptable error of $600?
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