1. Two balls are drawn in succession without replacement from an urn containing 4 red balls and 3 black balls. Find the probability distributionof the number of black balls.
2. It is said that happy and healthy workers are efficient and productive. A company that manufactures exercising machines wanted to know the percentage of large companies that provide on-site health club facilities. A sample of 240 such companies showed 96 of them provide such facilities on site.

i. Construct a 98% confidence interval for the percentage of all such companies that provide such facilities on-site. (4 marks)

ii. Find the maximum error of estimate in part (i).

1. An MP claims that the average number of acres in his province's State Parks is less than 2000 acres.A random sample of five parks is selected and the number of acres is shown below:

959, 1187, 493, 6249, 541

Assume the variable must be normally distributed, at= 0.01 is there enough evidence to support the claim?To draw your conclusion, state the hypotheses and identify the claim, find the critical value(s), label the acceptance and rejection region, calculate the test value and summarize the results.

1. Employees of a large corporation are concerned about the declining quality of medical services provided by their group health insurance. A random sample of 100 office visits by employees of this corporation to primary care physicians during the year 2017 found that the doctors spent an average of 19 minutes with each patient. This year a random sample of 108 such visits showed that doctors spent an average of 15.5 minutes with each patient. Assume that the standard deviations for the two populations are 2.7 and 2.1 minutes, respectively. Using the 2.5% level of significance, can you conclude that the mean time spent by doctors with each patient is lower for this year than for 2017? To draw your conclusion, state the hypotheses and identify the claim, find the critical value(s), label the acceptance and rejection region, calculate the test value and summarize the results.