Customer Arrivals

The following information was gathered from 100 families in rural KZN with regard to their weekly incomes.

1.1 Draw the downward sloping (<) ogive using the frequency distribution.     (3)

1.2 Calculate the mean weekly income.     (4)

1.3 Calculate the median income.     (3)

1.4 Calculate the mode.     (3)

1.5 Calculate the standard deviation.     (6)

1.6 Calculate the interquartile range     (6)

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)