## In a market study for Target, a researcher found that 70%

Question

Question 1: (6 marks)

In a market study for Target, a researcher found that 70% of customers are repeat customers. If 14 customers are selected at random, find the probability of getting.

Exactly 9 of them are repeat customers

At least 11 of them are repeat customers

At most 12 of them are repeat customers

Question 2: (4 Marks)

Using computer software (Excel, or calculation website) find the following probabilities and z values to 5 decimal places

P(zFind z0 such that P(z>z0)=0.12345

Question 3: (4 marks)

Scores are obtained from the Law School Admission Test (LSAT) are normally distributed with a mean score of 650 and a standard deviation of 120.

If a test score is selected at random, find the probability that it is less than 700.

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 4: (4 marks)

Assume that female students’ heights are normally distributed with a mean given by µ = 67.2 in. and a standard deviation given by ? = 3.6 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 5: (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 57.3?

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