Section 6.1 Problems 2, 6, & 10
2. Random Variables: Classification
Which of the following are continuous variables and which are discreet?
a. Speed of an airplane
b. Age of a college professor chosen at random
c. Number of books in the college bookstore
d. Weight of a football player chosen at random
e. Number of lightning strikes in Rocky Mountain National Park on a given day
6. History: Florence Nightingale
What was the age distribution of nurses in Great Britain at the tine of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from classic text Notes on Nursing, by Florence Nightingale). Note: in 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants.
Age Range (yr) 20-29 30-39 40-49 50-59 60-69 70-79 80+ Midpoint x 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Percent of nurses 5.7% 9.7% 19.5% 29.2% 25.0% 9.1% 1.8%
a. Using the midpoint x and the percentages of nurses, do we have a valid probability distribution? Explain.
b. Use a histogram to graph the probability distribution of part (a).
c. Find the probability that a British nurse selected at random in 1851 would be 60 years of age or older.
d. Compute the expected age of a British nurse contemporary to Florence Nightingale.
e. Compute the standard deviation for ages of nurses shown in the distribution.
10. Expected Value: Life Insurance
Sara is a 60 year old Anglo female in reasonably good health. She wants to take out a $50,000 term (that is, straight death benefit) life insurance policy until she is 65. The policy will expire on her 65th birthday. The probability of death in a given year is provided by the Vital Statistics section of the Statistical Abstract of the United States (116th Edition).
x= age (yrs) 60 61 62 63 64 P(death at this age) 0.00756 0.00825 0.00896 0.00965 0.01035