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The speeds at which drivers travel on a local highway follow a Normal distribution with mean 109 km/hour and standard deviation 7 km/hour.
1. The speeds at which drivers travel on a local highway follow a Normal distribution with mean 109 km/hour and standard deviation 7 km/hour. Law enforcement has concerns for the safety of travelers on this highway. The speed limit is 100 km/hour. Law enforcement does not consider 113 km/hour to be excessively over the speed limit though.
What proportion of drivers drive under 113 km/hour?
A. 0.2843
B. 0.5714
C. 0.7157
D. Not enough information for a valid answer.
2. Gainsborough Place is a subdivision of London, ON that began ten (10) years ago; the subdivision is currently comprised of 300 individual houses. A housing contractor hopes to build 20 more houses in the subdivision, but is in the planning stage. She is deciding how large to build the houses, and how much money they should be advertised for, based on the characteristics of the subdivision. To help in the decision process, she obtains sale price of a sample of 42 houses in the subdivision. The housing contractor constructed a histogram to summarize the resulting data.
Which of the following distributions is the best description of the histogram she created?
A. distribution of a variable for a sample
B. distribution of a variable for a population
C. sampling distribution (or approximation of one)
3. A large school district in southern California asked all its eighth-graders to measure the length of their right foot at the beginning of the school year, as part of a science project. The data demonstrated that foot length is approximately Normally distributed with mean of 23.4 cm, and standard deviation of 1.7 cm.
Suppose that a simple random sample of 25 eighth-graders from this population is selected. What is the probability that the mean foot length for this sample is between 22.5 and 23 cm?
A. 0.0040
B. 0.1071
C. 0.1150
D. 0.1190
E. Not enough information for a valid answer.
4. According to the National Institute of Allergy and Infectious Diseases in the United States, approximately 7% of American children 4 years of age or under have a food allergy that could result in life-threatening anaphylaxis. This is obviously a concern for day care providers that would be serving food to children.
Day cares maintained by the YMCA in the United States allow a maximum of 8 children aged 4 years or younger in their facilities. Consider the children aged 4 years or younger in a day care maintained by the YMCA in the United States as a simple random sample.
Which of the following options is the best description of the potential number of children aged 4 years or younger in such a daycare facility that have a food allergy?
A. Binomial distribution
B. Normal distribution (or approximately Normal)
C. Neither (approximately) Normal nor binomial distribution
5. Lovastatin is a medication prescribed by physicians to help decrease cholesterol level. The decrease in cholesterol after two months of taking the medication follows a Normal distribution with mean 80 mg/dL and standard deviation of 15 mg/dL. Very high decreases in cholesterol--in the upper 15% of the distribution--are associated with severe side effects; decreases in this range require a patient to change their medication from Lovastatin to something less aggressive.
What is the minimum decrease in cholesterol that results in a patient being required to change their medication? Answers have been rounded to one (1) decimal place.
A. 64.4 mg/dL
B. 81.0 mg/dL
C. 95.6 mg/dL
D. Not enough information for a valid answer.
