1. In a biology class, your final grade is based on several things: a lab score, scores on two major tests and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 25% of your total grade, each major test is worth 22.5% and the final exam is worth 30%. Compute your weighted class average for the following scores: 92 on the lab, 81 on the first major test, 93 on the second major test and 85 on the final exam.
2. Suppose that a certain data set has a bell-shaped distribution with µ = 13 and ó = 2. Between which two values would you expect to find about 95% of the data? If it were NOT known that the data had a bell-shaped distribution, what could you say about the percentage of data that lie between 7 and 19?
3. If you roll two fair six-sided dice, what are the odds in favor of the two dice showing a sum of 5?
4. If five people are randomly selected, what is the probability that at least two of them share the same birthday? Assume 365 days per year.
5. If there is a 40% chance of rain today and a 50% chance of rain tomorrow, what is the probability that it will rain today OR tomorrow?
6. Six men attend a party and each leaves their hat at the door. If, at the end of the evening, the hats are randomly returned to the men, what is the probability that each man receives his own hat?
7. A jury pool consists of 10 men and 10 women. If a jury of 12 is to be randomly selected, how many juries are possible which contain 7 men and 5 women?
8. You are dealt five cards, without replacement , from a standard deck (52 cards). What is the probability that you are dealt exactly four face cards?
9. A game of chance consists of the following: Two fair six-sided dice are rolled. If the two dice show a sum of 8, you win $10. Otherwise, you have to pay $3. Find your expected value for one game.
10. In a recent survey, 70% of single men indicated that they would welcome a woman taking the initiative in asking for a date. A random sample of 20 single men was asked if they would welcome a woman taking the initiative in asking for a date. What is the probability that at least 18 of the men will say yes?
11. Susan is taking Western Civilization this semester on a pass/fail basis. The department teaching the course has a history of passing 77% of the students in the course each term. What is the probability that Susan needs three or more tries to pass Western Civilization?
12. Parkfield, California, is dubbed the world's earthquake capital because it sits on top of the notorious San Andreas fault. Since 1857, Parkfield has had a major earthquake on the average of once every 22 years. Find the probability that Parkfield will have more than two major earthquakes in the next 60 years.
13. Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village were approximately normally distributed with a mean of 5.1 mm and a standard deviation of 0.9 mm. For a randomly found shard, what is the probability that the thickness is between 3.0 mm and 7.0 mm?
14. Suppose that X is normally distributed with µ = 12.4 and ó = 0.93. Find P30 and Q3
15. The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. If 25 randomly selected women are put on a special diet just before they become pregnant, find the probability that their lengths of pregnancy have a mean that is less than 260 days. If the 25 women DO have a mean of less than 260 days, does it appear that the diet has an effect on the length of pregnancy? Why or why not?
16. A Boeing 767 aircraft has 213 seats. When someone buys a ticket for a flight, there is a 0.0995 probability that the person will not show up for the flight. A ticket agent accepts 236 reservations for a flight that uses a Boeing 767. Find the probability that not enough seats will be available. Is this probability low enough so that overbooking is not a real concern?
17. A simple random sample of 50 adults (males and females) is obtained, and each person's red blood cell count (in cells per microliter) is measured. The sample mean is 4.63 and the sample standard deviation is 0.54. Construct a 95% confidence interval for the mean red blood cell count of all adults.
18. The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. If a single fan blade broke during operation, it could severely endanger a flight. A large engine contains thousands of fan blades, and safety regulations require that variability measurements on the population of all blades not exceed ó 2 = 0.15 mm 2 . An engine inspector took a random sample of 61 fan blades from an engine. She measured each blade and found a sample variance of 0.17 mm 2. Find a 95% confidence interval for the population variance. Should the fan blades be replaced? Why or why not?
19. Let x be a random variable that represents milliliters of oxygen per deciliter of whole blood. For healthy adults, the population mean of x is ì = 19.0 milliliters of oxygen per deciliter. A company that sells vitamins claims that its multivitamin complex will increase the oxygen capacity of the blood. A random sample of 48 adults took the vitamins for 6 months. After blood tests, it was found that the sample mean was x-bar = 20.7 milliliters of oxygen per deciliter with a sample standard deviation s = 9.9. Use a 1% level of significance to test the claim that the average oxygen capacity has been increased.
20. A Pennsylvania study concerning preference for outdoor activities used a questionnaire with a 6-point Likert-type response in which 1 designated "not important" and 6 designated " extremely important". A random sample of n 1 = 122 adults was asked about lake fishing as an outdoor activity. The mean response was x̅ 1 = 4.3 with sample standard deviation s 1 = 1.3. Another random sample of n 2 = 104 adults was asked about stream fishing as an outdoor activity. For this group, the mean response was x̅ 2 = 4.0 with s 2 = 1.3. At the 1% significance level, do these data indicate that the population mean preference for lake fishing is greater than the population mean preference for stream fishing?
21. Based on information from Harper's Index, 37 out of a random sample of 100 adult Americans who did not attend college believe in extraterrestrials. However, out of a random sample of 100 Americans who did attend college, 41 claim that they believe in extraterrestrials. At the 1% significance level, does this indicate that the proportion of people who attended college who believe in extraterrestrials is higher than the proportion who did not attend college?
22. The Fish and Game Department stocked Lake Lulu with fish in the following proportions: 30% catfish, 15% bass, 40% bluegill and 15% pike. Five years later they sampled the lake to see if the distribution of fish had changed. They found the 500 fish in the sample were distributed as follows:
CATFISH 120
BASS 85
BLUEGILL 220
PIKE 75
In the five-year interval, did the distribution of fish change at the 0.05 level?