Street Vendor

2.1 On weekdays from 11: 30 am to 2:00 pm customers arrive at a hotdog street vendor at the rate of 25 per 30 minute interval. Assume that this process can be well modeled by the Poisson distribution.
2.1.1 What is the average time between customer arrivals?     (2)
2.1.2 What is the probability that the vendor will have to wait no more than 3 minutes for a customer?     (3)
2.2 In a survey conducted by the Society for human Resource Management, 68% of workers said that employers have the right to monitor their telephone use. Suppose that a random sample of 20 workers is selected, and they are asked if employers have the right to monitors telephone use. What is the probability that:
 2.2.1 5 or less of the workers agree?     (3)
2.2.2 15 or less of the workers agree?     (4)
2.3 The birth weights of female babies born at a certain hospital are approximately normally distributed with a mean of 3.40kg and a standard deviation of 0.48 kg. Find the proportion of female babies who have birth weights in the following ranges:
2.3.1 less than 3.94 kg     (2)
2.3.2 more than 2.96 kg     (3)
2.33 between 2.5 kg and 3.70 kg      (3)
2.4 Referring to question 2.3 above, if the Babies are to be defined as ‘underweight’ when they are in the lowest 5%of the distribution, what will be the cut-off point defining underweight?     (5)
3.1 A shopkeeper observes the number of cans of cool drink of various types sold during one week. The results are displayed in the table below:


Screenshot from 2018-04-25 11-39-58

Test with 5% level of significance if there is any relationship between the days of the week and popularity of the various types of soft drink    (12)

3.5 The results of an annual claimant satisfactory Survey of policyholders who have had claim with State Farm Insurance Company revealed a 90%
satisfactory rate for claim rate for service. To check the accuracy of this claim, a random sample of State farm claimants was asked to rate whether they were satisfied with the quality of the service. The number who were satisfied was 153, unsatisfied 24. Test at the 5% significance level that the satisfaction rate is less than 90%.     (8)

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