Homework 6 questions:

Question 1 1.25 pts A random variable is normally distributed with a mean of p = 39 and a standard deviation of o = 10.8. Calculate the Z-score for a value of 32. For all answers involving decimal places, answer to four decimal places AND include the zero before the decimal places, e.g. 0.1110. Q Question 2 1.25 pts A random variable is normally distributed with a mean of p = 48 and a standard deviation of o = 23.8. Calculate the Z-score for a value of 29. Question 3 1.25 pts A random variable is normally distributed with a mean of p = 37 and a standard deviation of o = 13.6. Calculate the Z-score for a value of 57. S Question 4 1.25 pts A random variable is normally distributed with a mean of p = 30 and a standard deviation of o = 5. What is the probability that the random variable will assume a value between 25 and 35? For all answers involving decimal places, answer to four decimal places AND include the zero before the decimal places, e.g. 0.1110. : Question 5 1.25 pts A random variable is normally distributed with a mean of p = 30 and a standard deviation of o = 5. What is the probability that the random variable will assume a value that is less than 20? Make sure your answer is between 0 and 1. Question 6 1.25 pts Given that z is a standard normal random variable, compute the probability that it takes on a value between 1.96 and 1.96. Make sure your answer is between 0 and 1. S Question 7 1.25 pts Given that z is a standard normal random variable, compute the probability that it takes on a value less than 2. For all answers involving decimal places, answer to four decimal places AND include the zero before the decimal places, e.g. 0.1110. S Question 8 1.25 pts Given that z is a standard normal random variable, compute the probability that it takes on a value that is either greater than 2 or less than -2. For all answers involving decimal places, answer to four decimal places AND include the zero before the decimal places, e.g. 0.1110. S Question 9 1.25 pts Given that z is a standard normal random variable, compute the probability that it takes on a value between 1 and 3. For all answers involving decimal places, answer to four decimal places AND include the zero before the decimal places, e.g. 0.1110. S Question 10 1.25 pts Given that z is a standard normal random variable, find the z-score for a situation where the area to the left of z is equal to 0.8907. For all answers involving decimal places, answer to four decimal places AND include the zero before the decimal places, e.g. 0.1110. E 1:) Question 11 1.25 pts Given that z is a standard normal random variable, find the z-score for a situation where the area to the left of z is 0.0901. For all answers involving decimal places, answer to TWO decimal places, include the zero before the decimal places, and the negative sign when needed e.g. -0.10 D Question 12 1.25 pts Every day Cara runs for five miles. Suppose that the time it takes her to complete the run is a random variable that is normally distributed with a mean of 60 minutes and a standard deviation of 5 minutes. Today Cara ran the five miles in 51 minutes. What is the probability that she will beat her time tomorrow? For all answers involving decimal places, answer to four decimal places AND include the zero before the decimal places, e.g. 0.1110. Q D Question 13 1.25 pts A person must score in the upper 2% of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 10, what score must a person have to qualify for Mensa? For all answers involving decimal places, answer to four decimal places. Hint: you are not calculating probabilities. D Question 14 1.25 pts Suppose that the mean cost of domestic airfares in the United States is $399 per ticket, with a standard deviation of $119. If domestic airfares are normally distributed, what is the cost for the highest 5% of domestic airfares? Q D Question 15 1.25 pts Suppose that the average person watches 6.25 hours of television per day with a standard deviation of 2.75 hours. Assuming television viewing is normally distributed, what percentage of people watch over 10 hours of television per day? (Use Excel to solve this question) For all answers involving decimal places, answer to four decimal places. Hint: you are not calculating probabilities, but the percentage. D Question 16 1.25 pts The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. If students have only 100 minutes to complete the exam, what percentage of the class will not finish the exam on time? For all answers involving decimal places, answer to four decimal places. Hint: you are not calculating probabilities, but the percentage. D Question 17 1.25 pts In New York City the average hotel room costs $234 per night, with a standard deviation of $65. Suppose that you walk into a random hotel and learn their rate is $155 per night. If the rates are normally distributed, what is the probability that if you leave and walk into another random hotel, they will have a lower rate? For all answers involving decimal places, answer to four decimal places, AND include the zero before the decimal places, e.g. 0.1110. Question 18 1.25 pts Suppose that height is normally distributed with a mean of 68 inches and a standard deviation of 4 inches. How many inches tall are the tallest 3% of people? For all answers involving decimal places, answer to four decimal places. Hint: you are not calculating probabilities. Question 19 1.25 pts Suppose that a bank keeps $13,000 in deposits available for their customers to withdraw each day. The average net withdrawals for the bank are $9,000 with a standard deviation of $1,500. It net withdrawals are normally distributed, what is the probability that the bank will not be able to meet customer demands on any given day? For all answers involving decimal places, answer to four decimal places, AND include the zero before the decimal places, e.g. 0.1110. S Question 20 1.25 pts Given that z is a standard normal random variable, compute the probability that it takes on a value between -2 and -1. For all answers involving decimal places, answer to four decimal places, AND include the zero before the decimal places, e.g. 0.1110. S