Assignment:
Q1) Assume a binomial probability distribution with n= 40 and πI = 0.55.
Compute the following: (Round the value for standard deviation and intermediate calculations to 2 decimal places and your final answer to 4 decimal places.)
(a) The mean and standard deviation of the random variable.
?=
I =
(b) The probability that X is 25; or greater.
(c) The probability that X is 15; or less.
(d) The probability that X is between 15 and 25 inclusive.
Q2)It is estimated that 10 percent of those taking the quantitative methods portion of the CPA examination fail that section. Sixty students are taking the exam this Saturday.
(a-1) How many would you expect to fail?
(a-2) What is the standard deviation? (Round your answer to 2 decimal places.)
(b) What is the probability that exactly two students will fail? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)
(c) What is the probability that at least two students will fail? (Round your answer to 4 decimal places.)
Q3.)The Oil Price Information Center reports the mean price per gallon of regular gasoline is $3.79 with a population standard deviation of $0.18. Assume a random sample of 40 gasoline stations is selected and their mean cost for regular gasoline is computed.
(a) What is the standard error of the mean in this experiment? (Round your answer to 4 decimal places.)
(b) What is the probability that the sample mean is between $3.77 and $3.81? (Round z value to 2 decimal places.Round your final answer to 4 decimal places.)
(c) What is the probability that the difference between the sample mean and the population mean is less than 0.01? (Round z value to 2 decimal places. Round your final answer to 4 decimal places.)
(d) What is the likelihood the sample mean is greater than $3.87? (Round z value to 2 decimal places. Round your final answer to 4 decimal places.)
Q4)CRA CDs, Inc., wants the mean lengths of the "cuts" on a CD to be 135 seconds (2 minutes and 15 seconds). This will allow the disk jockeys to have plenty of time for commercials within each 10-minute segment. Assume the distribution of the length of the cuts follows the normal distribution with a population standard deviation of 8 seconds. Suppose we select a sample of 16 cuts from various CDs sold by CRA CDs, Inc.
(a) What can we say about the shape of the distribution of the sample mean?
(b) What is the standard error of the mean?
(c) What percent of the sample means will be greater than 140 seconds? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)
(d) What percent of the sample means will be greater than 128 but less than 140 seconds? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)
Q5.)A normal population has a mean of 75 and a standard deviation of 5. You select a sample of 40.
Compute the probability the sample mean is (Round your z values to 2 decimal places and final answers to 4 decimal places):
(a) Less than 74.
(b) Between 74 and 76.
(c) Between 76 and 77.
(d) Greater than 77.
Provide complete and step by step solution for the question and show calculations and use formulas.