Question 1
Scores are obtained from Law School Admission Test are normally distributed with a mean score of 550 and a standard deviation of 110.
If a test score is chosen at random, determine the probability that it is less than 750.
If the top 15 percent of the test scores are usually good enough for admission to law school, evaluate the cut off score for gaining admission.
Question 2:
Consider that female students' heights are normally distributed with a mean provided by µ = 64.2 in. and a standard deviation given by σ = 2.6 in.
If one female student is randomly picked, determine the probability that her height is above 63.0 in.
If 100 female students are randomly picked, evaluate the probability that they have a mean height greater than 63.0 in.
Question 3:
As part of his review for a chemistry test, a student randomly picks (without replacement) 40 out of 102 elements listed on the standard tables, and tries to guess their atomic numbers. Provided that the mean of all 102 atomic numbers is 51.794, and the population standard deviation is 29.804, Find the probability that the mean of the 40 atomic numbers selected by the student will be at least 58.3?
Question 4:
A random sample of 250 Ontario households by natural gas heating show that the mean monthly consumption of gas is 107.73 cu. ft., with a standard deviation of 13.94 cu. ft. Use these statistics to prepare a 94% confidence interval for the mean monthly consumption for the population of all Ontario households.
Question 5:
A psychologist has to prepare a new test of spatial perception, and she wants to evaluate the mean score achieved by male pilots. How many people must she test if she wants sample mean to be in error by no more than 2.0 points, with 95 percent confidence? An earlier study suggests that σ = 21.2.
Question 6:
In a study relating amounts of time required for room service delivery at a newly opened Radisson Hotel, 20 deliveries had a mean time of 24.2 min and a standard deviation of 8.7 min. The sample data seems to have a bell-shaped distribution. Evaluate the 90 percent confidence interval for the mean time of all deliveries.