Clearly state what the random variable in this problem is? b.

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Sep 19, 2022

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Presenting only the final answer is not sufficient to get complete credit. Show the steps in solution approach. That way partial credit can be earned to various steps in final solution. It is your responsibility to demonstrate mastery of the subject matter through your answers. 3) Submit your report as an Excel file. Solve each problem on a separate tab (worksheet). Organize your solutions on the Excel worksheet properly. Show where your answers are for each problem and the sections of the problem. Use proper formatting. Name Your File to show your Full Name and the HW Number. Upload your report file on Canvas and verify if everything is fine by opening up the uploaded file. It is your responsibility to ensure your report is uploaded properly. 4) Do not wait until the last minute. The deadline is strictly enforced by Canvas. No hardcopy submissions are accepted. No e-mail submissions are accepted. If your file does not appear on Canvas by the deadline, zero points will be recorded for you for that HW. No exceptions are entertained for any reason under any circumstance in this regard. HW Problems: 1) If a random variable X is normally distributed with a mean=60 and a standard deviation=15, compute the following probabilities. a. P(X > 60) = b. P(X > 75) = c. P(X > 80) = d. P(X < 50) = e. P(45 < X < 75) = f. P(X < 45) = 2) Given that z is a standard normal random variable, compute the following probabilities. a. P(Z ≤ -1.09) = b. P(Z ≤ -1.5) = c. P(Z ≥ 1.3) = d. P(Z ≥ 2.54) = e. P(-0.71 z0) = 0.12; what is z0 = b. If P(Z z0) = 0.25; what is z0 = d. If P(Z < z0) = 0.3; what is z0 = 4) Given that Z is a standard normal random variable (follows as Standard Normal Distribution), find z. a. If the area to the left of z is 0.9750, then what is z = 2 b. If the area between 0 and z is 0.4750 then what are the possible values for z = c. If the area to the left of z is 0.7291, then what is z = d. If the area to the right of z is 0.1314, then what is z = e. If the area to the left of z is 0.6700, then what is z = f. If the area to the right of z is 0.3300, then what is z = 5) The letter grades on the midterm exam given in a large managerial statistics class are normally distributed with mean 75 and standard deviation 9. The instructor of this class wants to assign an A grade to the top 10% of the scores, a B grade to the next 10% of the scores, a C grade to the next 10% of the scores, a D grade to the next 10% of the scores and an F grade to all scores below the 60th percentile of this distribution. For each possible letter grade, find the lowest acceptable score. 6) The time needed to complete a final examination in a particular college course is normally distributed with a mean of 90 minutes and a standard deviation of 15 minutes. Answer the following questions. a. What is the probability of completing the exam in one hour or less? b. What is the probability that a student will complete the exam in more than 60 minutes but less than 105 minutes? c. Assume that the class has 60 students and that the examination period is 120 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time? 7) For borrowers with good credit scores, the mean debt for revolving and installment accounts is $15,015. Assume the standard deviation is $3,540 and that debt amounts are normally distributed. a. What is the probability that the debt for a borrower with good credit is more than $18,000? b. What is the probability that the debt for a borrower with good credit is less than $10,000? c. What is the probability that the debt for a borrower with good credit is between $12,000 and $18,000? d. What is the probability that the debt for a borrower with good credit is no more than $14,000? 8) In an article about the cost of health care, Money magazine reported that a visit to a hospital emergency room for something as simple as a sore throat has a mean cost of $328. Assume that the cost for this type of hospital emergency room visit is normally distributed with a standard deviation of $92. Answer the following questions about the cost of a hospital emergency room visit for this medical service. a. What is the probability that the cost will be more than $500? b. What is the probability that the cost will be less than $250? c. What is the probability that the cost will be between $300 and $400? d. If the cost to a patient is in the lower 8% of charges for this medical service, what was the cost of this patient’s emergency room visit? 9) The average night’s sleep for a grown-up adult is 6.8 hours. Assuming the probability distribution of the sleep time to be normal with a standard deviation of 0.8 hours, compute the following. a. Clearly state what the random variable in this problem is? b. What is an appropriate distribution to be used for this problem and why? c. What is the probability that a randomly selected person sleeps for more than 8 hours? d. What is the probability that a randomly selected person sleeps 6 hours or less? e. Doctors recommend that a person get between 7 and 9 hours of sleep each night. What percentage of the population gets recommended levels of sleep?

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