Chapter 6
- For borrowers with good credit scores, the mean debt for revolving and installment accounts is$15,015. Assume the standard deviation is $3540 and the debt amounts are normally distributed.
- What is the probability that the debt for a borrower with good credit is more than $18,000?
- What is the probability that the debt for a borrower with good credit is less than $10,000?
- What is the probability that the debt for a borrower with good credit is between $12,000 and $18,000?
- What is the probability that the debt for a borrower with good credit is no more than $14,000?
- In an article about 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. Assume that the following questions about the cost of a hospital emergency room visit for this medical service.
- What is the probability that the cost will be more than $500?
- What is the probability that the cost will be less than $250?
- What is the probability that the cost will be between $300 and $400?
- 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?
- A person must score in the upper 2% of the population on an IQ test to qualify for member ship in Mensa, the international high-IQ society. If IQ scores are normally distributes with a mean of 100 and a standard deviation of 15, what score must a person have to qualify for Mensa?
- The time required 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. Answer the following questions.
- What is the probability of completing the exam in an hour or less?
- What is the probability that a student will complete in more than 60 minutes but less than 75 minutes?
- Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time?
- According to the Sleep Foundation, the average night’s sleep is 6.8 hours. Assume the standard deviation is 0.6 hours and the probability distribution is normal.
- What is the probability that a randomly selected person sleeps more than 8 hours?
- What is the probability that a randomly selected person sleeps 6 hours or less?
- Doctors suggest getting between 7 and 9 hours of sleep each night. What percentage of the population gets this much sleep?
- Conde’ Nast Traveler publishes a Gold List of the top hotels all over the world. The Broadmoor Hotel in Colorado Springs contains 700 rooms and is on the 2004 Gold List. Suppose Broadmoor’s marketing group forecasts a mean demand of 670 rooms for the coming weekend. Assume that demand for the upcoming weekend is normally distributed with a standard deviation of 30.
- What is the probability that all the hotel’s room will be rented?
- What is the probability 50 or more rooms will not be rented?
- Would you recommend the hotel consider offering a promotion to increase demand? What considerations would be important?
- Is lack of sleep causing traffic fatalities? A study conducted under the auspices of the National Highway Traffic Safety Administration found that the average number of fatal crashes caused by drowsy drivers each year was 1500. Assume the annual number of fatal crashes per year is normally distributed with a standard deviations of 300.
- What is the probability of fewer than 1000 fatal crashes in a year?
- What is the probability the number of fatal crashes will be between 1000 and 2000 for a year?
- For a year to be in the upper 5% with respect to the number of fatal crashes, how many crashes would have to occur?