Statistics for the Social and Management Sciences
Please prepare the answers to the following questions as neatly as you can. Do the work manually (no computers) and show your complete work.
Of the total employees of an organization only 30% are covered for life insurance. Five employees from this organization are randomly selected. Find the probability that
None of the employees have life insurance.
Exactly two employees have life insurance.
At most three employees have life insurance.
At least four employees have life insurance.
If X represents the number of employees (of the selected five) who have life insurance, show different values of X and its probability, P(X), in a probability distribution table.
Produce a probability distribution graph from the table in part (e), and comment on the shape of this distribution.
A brand of tire is guaranteed to last an average of 25,000 kilometers. The average life of a random sample of 36 such tires was found to be 24,000 kilometers. Assume that the tire life is normally distributed with a standard deviation of 500 kilometers. Do you think you could successfully sue the company for false advertising? (Be careful!)
It is believed that 55% of the students own laptop computers. A random sample of 300 students revealed that 155 of them had laptop computers. Is there evidence that the percentage of students with laptop is more than 55%?
The cafeteria manager claims that 70% of its customers are happy with the quality and price of the food it serves. In a random sample of 500 cafeteria customers, 320 say they are happy with the cafeteria. Does the sample result suggest that fewer than 90% of the customers are happy with the quality and price of the food? Complete a formal hypothesis test using a = 5%.
A random survey of 30 countries across the world yielded an average life expectancy of 62 years with a standard deviation of 6 years. The data appear to be normally distributed. Construct
a 99% confidence interval for the average life expectancy of countries around the world.
a 95% confidence interval for the average life expectancy of countries around the world.
a 90% confidence interval for the average life expectancy of countries around the world.
Comment on the relationship between the level of confidence and the length of the interval.
Hint: Use the Standard Normal Table to calculate p-values, and z-scores as needed.

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