The marketing manager of a branch office of a local telephone operating company wants to study characteristics of residential customers served by her office. In particular, she wants to estimate the mean monthly cost of calls within the local calling region. In order to determine the sample size necessary, she needs an estimate of the standard deviation. On the basis of her past experience, she estimates that the standard deviation is equal to $12. Suppose that a small scale study of 15 residential customers indicates a sample standard deviation of $9.25. At the 0.10 level of significance, is there evidence that the population standard deviation is less than $12?
The local Office of Tourism sells souvenir calendars. Sue, the head of the office, needs to order these calendars in advance of the main tourist season. Based on past seasons, Sue has determined the probability of selling different quantities of the calendars for a particular tourist season. Demand for Calendars Probability of Demand 75,000 0.15 80,000 0.25 85,000 0.30 90,000 0.20 95,000 0.10 The Office of Tourism sells the calendars for $12.95 each. The calendars cost Sue $5 each. The salvage value is estimated to be $0.50 per unsold calendar. Determine how many calendars Sue should order to maximize expected profits
The test scores on a 100-point test were recorded for 20 students: 71 73 84 77
a.) Can you reasonably assume that these test scores have been selected from a normal population? Use a stem and leaf plot to justify your answer.
b.) Calculate the mean and standard deviation of the scores.
c.) If these students can be considered a random sample from the population of all students, find a 95% confidence interval for the average test score in the population.
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