Scores are obtained from the Law School Admission Test (LSAT) are normally distributed with a mean score

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Question:

Scores are obtained from the Law School Admission Test (LSAT) are normally distributed with a mean score of 550 and a standard deviation of 110.

If a test score is selected at random, find the probability that it is less than 750.
If the top 15% of the test scores are usually good enough for admission to law school, find the cut off score for gaining admission.

Question 2: (4 marks)
Assume that female students’ heights are normally distributed with a mean given by µ = 64.2 in. and a standard deviation given by σ = 2.6 in.

If one female student is randomly selected, find the probability that her height is above 63.0 in.
If 100 female students are randomly selected, find the probability that they have a mean height greater than 63.0 in.

Question 3: (3 marks)
As part of his review for a chemistry test, a student randomly selects (without replacement) 40 out of 102 elements listed on the standard tables, and tries to guess their atomic numbers. Given that the mean of all 102 atomic numbers is 51.794, and the population standard deviation is 29.804, what is the probability that the mean of the 40 atomic numbers selected by the student will be at least 58.3?

Question 4: (3 marks)
A random sample of 250 Ontario households using natural gas heating show that the mean monthly consumption of natural gas is 107.73 cu. ft., with a standard deviation of 13.94 cu. ft. Use these statistics to construct a 94% confidence interval for the mean monthly consumption for the population of all Ontario households.

Question 5: (3 marks)
A psychologist has to develop a new test of spatial perception, and she wants to estimate the mean score achieved by male pilots. How many people must she test if she wants the sample mean to be in error by no more than 2.0 points, with 95% confidence? An earlier study suggests that σ = 21.2.

Question 6: (3 marks)
In a study relating the 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 appears to have a bell-shaped distribution. Find the 90% confidence interval for the mean time of all deliveries.