Stats test 2

Suppose that you arrive at a bus stop randomly, so all arrival times are equally likely. The bus arrives regularly every 60 minutes without delay. What is the expected value of your waiting time? Objective: (6.3) Find Expected Value

30 min

Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling a 4 or a 1, nothing otherwise. What is your expected value of your gain or loss? Objective: (6.3) Find Expected Value

$0.00

At an intersection in Normal, Illinois, there were 90 vehicle accidents with 168,276 vehicles passing through the intersection. Determine the accident rate per 1000 vehicles. Objective: (6.4) Determine Rate per Standard Amount

0.535 accident per 1000 vehicles

Human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. If 19 people are randomly selected, find the likelihood that their mean body temperature will be less than 98.40°F. Objective: (5.3) Solve Apps: Find Likelihood of Sample Means

0.9192

In an analysis of the accuracy of weather forecasts, the actual high temperatures are compared to the high temperatures predicted one day earlier and the high temperatures predicted one week earlier. Listed below are the errors between the predicted temperatures and the actual high temperatures for consecutive days in North Town. Do the standard deviations suggest that the temperatures predicted a day in advance are more accurate than those predicted a week in advance? Number 4

) One day: range = 11 degrees; standard deviation = 2.38 degrees One week: range = 16 degrees; standard deviation = 3.87 degrees There appears to be greater variation in errors from the one-week forecast (as we might expect).

A 28-year-old man pays $173 for a one-year life insurance policy with coverage of $ 50,000. If the probability that he will live through the year is 0.9993, what is the expected value for the insurance policy? Objective: (6.3) Find Expected Value

-$138.00

At an intersection in Normal, Illinois, there were 90 vehicle accidents with 167,238 vehicles passing through the intersection. Determine the accident rate per 100 vehicles. Objective: (6.4) Determine Rate per Standard Amount

0.054 accident per 100 vehicles

A final exam in Math 160 has a mean of 73 with standard deviation 8.16. Assume that a random sample of 24 students is selected and the test score of the sample is computed. Assuming the scores are normally distributed, what percentage of sample means are greater than 78? Objective: (5.3) Solve Apps: Find Percentage of Sample Means

0.13%

The scores on a certain test are normally distributed with a mean score of 69 and a standard deviation of 2. What is the likelihood that a sample of 90 students will have a mean score of at least 69.2108? Objective: (5.3) Solve Apps: Find Likelihood of Sample Means

0.1587

Suppose The that after 50 at-bats a baseball player has a batting average of 0.400. If the baseball player gets a hit at the next at-bat, what will the player's new batting average be? (The batting average is the number of hits divided by the number of at-bats.) Objective: (4.1) Solve Apps: Mean

0.412

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 101 inches, and a standard deviation of 16 inches. What is the likelihood that the mean annual precipitation during 64 randomly picked years will be less than 103.8 inches? Objective: (5.3) Solve Apps: Find Likelihood of Sample means

0.9192

What is the death rate due to liver disease in deaths per 1,000,000 people?

108 deaths per 1,000,000 people

In 2003, the population of Gabon was 1,321,560 people. The death rate was 11.17 per 1000 people. About how many deaths were there in Gabon in 2003? Objective: (6.4) Determine Birth/Death Rate

14,762 deaths

The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the cars it makes. Suppose that the models and mpg's for a manufacturer are Corsair (8 mpg), Futura (13 mpg), Retro (15 mpg), and Envy (26 mpg). Twenty percent of the cars sold are Corsairs, 30% are Futuras, 40% are Retros, and 10% are Envys. Find the average mpg for this manufacturer. Objective: (4.1) Solve Apps: Calculate Weighted Average

14.1 mpg

A six-mile trip of Sprinkle Road had 51 traffic fatalities last year. There were 2.9 million miles driven along this stretch. Determine the traffic fatality rate per 1,000,000 miles driven. Round your answer to hundredths. Objective: (6.4) Determine Rate per Standard Amount

17.59 deaths per 1,000,000 miles driven

The following data set is the GPA's of the students in a statistics class. 1.93, 1.99, 2.00, 2.04, 2.12, 2.34, 2.55, 2.55, 2.75, 2.75, 2.80, 2.80, 2.85, 3.02, 3.12, 3.22, 3.31, 3.33, 3.45, 3.69 What value is the 25th percentile

2.12

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches? Objective: (5.2) Use Normal Distribution

2.28%

One common system for computing a grade point average (GPA) assigns 4 points to an A, 3 points to a B, 2 points to a C, and 1 point to a D. What is the GPA of a student who gets a B in a 3-credit course, an A in a 2-credit course, and a B, a B, and a D, respectively, in each of three 4-credit courses? Round your answer to the nearest hundredth.

2.65

Suppose that your income is at the 76th percentile of wage earners in the United States. What percent of wage earners make more than you? 8) Objective: (4.3) Solve Apps:

24%

Scores on an English test are normally distributed with a mean of 30.8 and a standard deviation of 6. Find the 41st percentile. Round your answer to one decimal place. Objective: (5.2) Find Percentile

29.4

What is the probability of getting two tails and one head when you toss three fair coins at once? Objective: (6.2) Solve Apps: Probability Distrubutions

3/8

The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the models it makes. Suppose that the mpg's for four of the the five models of a manufacturer are 17, 24, 32, and 24, and the manufacturer just meets the government standard of 26 mpg. Find the mileage for the fifth model Find the Mean

33 Mpg

The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the models it makes. Suppose that the mpg's for the five models of a manufacturer are 19, 21, 22, 28, and 18, and the government requirement is 24 mpg. The last of the models is to be redesigned to meet the government requirement. What must the new mpg of this model be to meet the requirement?

36 mpg

Suppose that there are 400 students in your school class. What class rank is the 10th percentile?

40

The volumes of soda in quart soda bottles are normally distributed with a mean of 32 ounces and a standard deviation of 1.2 ounces. What percentage of soda bottles will have a volume less than 31.70 ounces? Objective: (5.2) Use Normal Distribution

40.13%

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. What percentage of the ratings will be between 160 and 230? 52) Objective: (5.2) Use Normal Distribution

51.38%

The monthly incomes of trainees at a local mill are normally distributed, with a mean of $1,100 and a standard deviation $150. What percentage of trainees earn less than $875 a month? Objective: (5.2) Use Normal Distribution

6.68%

The systolic blood pressure of a group of 18-year-old women is normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women in this group have a systolic blood pressure between 108 mmHg and 132 mmHg? Objective: (5.2) Apply the 68-95-99.7 Rule

68%

The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.Assume that a random sample of 25 pregnant woman is selected and the mean is computer. What percentage of sample means will be between 265 and 271 days? Objective: (5.3) Solve Apps: Find Percentage of Sample Mean

68.26%

The host of a dinner party purchases wine based on the weighted average of clarity (6%), bouquet (7%), friendliness to the palate (7%), storageability of opened bottles (40%), and price (40%). Suppose that Bone Ranch Wave has scores in these categories of 4, 5, 3, 8, and 9, respectively. What is its rating? Objective: (4.1) Solve Apps: Calculate

7.60

The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the models it makes. Suppose that the average mpg for the four models manufactured is 21 mpg and the government standard is 33 mpg. The manufacturer will add a model. What mileage must the new model get so that the manufacturer meets the government requirement Objective: (4.1) Solve Apps: Mean

81 mpg

The course grade in a statistics class is the average of the scores on five examinations. Suppose that a student's scores on the first four examinations (out of 100) are 75, 71, 87, and 77. What is the highest course average possible after the last examination? Objective: (4.1) Solve Apps: Mean

82

An insurance company reported that last year there were claims for medical expenses for 2821 on-the-job injuries. The company covers 328,272 employees. Find the rate of on-the-job injuries per 10,000 employees. Round your answer to hundredths. Objective: (6.4) Determine Rate per Standard Amoun

85.93 injuries per 10,000 employees

Your course grade is based on one midterm that counts as 20% of your final grade, a set of quizzes that counts as 15% of your final grade, a set of homework assignments that counts as 35% of your final grade, and a final exam that counts as 30% of your final grade. Your midterm score is 83, your quiz score is 84, your homework score is 99, and your final exam score is 95. What is your overall final score? Objective: (4.1) Solve Apps: Calculate Weighted Average

92.35

The annual precipitation for one city is normally distributed with a mean of 261 inches and a standard deviation of 3 inches. What percentage of years had precipitation between 255 inches and 267 inches? Objective: (5.2) Apply the 68-95-99.7 Rule

95%

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 230 hours and a standard deviation of 11 hours. What percentage of the bulbs have lifetimes that lie within 2 standard deviations to either side of the mean? Objective: (5.2) Apply the 68-95-99.7 Rule

95%

A final exam in Math 160 has a mean of 73 with standard deviation 7.73. Assume that a random sample of 24 students is selected and the test score of the sample is computed. Assuming the scores are normally distributed, what percentage of sample means are less than 76? Objective: (5.3) Solve Apps: Find Percentage of sample means

97.13%

The amount of Jen's monthly phone bill is normally distributed with a mean of $61 and a standard deviation of $9. What percentage of her phone bills are between $34 and $88? Objective: (5.2) Apply the 68-95-99.7 Rule

99.7%

A gambler playing blackjack in a casino has lost each of his first 189 bets. If he correctly understood the Law of Large Numbers, which strategy would he use in betting on future blackjack hands? a. He should bet based on the merit of each individual hand. While the proportion of wins should eventually approach the true probability of winning, this does not mean that he is likely to recover early losses. b. He should bet more on the next 189 hands, because the proportion of wins should quickly approach the true probability of winning. b. He should bet less on the next 189 hands, because it doesn't look like this is a good day for him. d. He shouldn't use any of the above strategies.

A

The following data set is the GPA's of the students in a statistics class. 1.93, 1.99, 2.00, 2.04, 2.12, 2.34, 2.55, 2.55, 2.75, 2.75, 2.80, 2.80, 2.85, 3.02, 3.12, 3.22, 3.31, 3.33, 3.45, 3.69 What percentile is a GPA of 2.34

About the 30th

Jim has been stopped for speeding four times in the last year, but each time was given a warning instead of a ticket. What does it mean to say that "the law of averages will catch up with him"? a. It means that average drivers receive tickets, not warnings, when stopped for speeding. b. It means that Jim is "due" to receive a ticket next time he is stopped for speeding. c. It means that, in the long run, Jim should not expect to be stopped for minor speeding violations. d. None of the above is a correct interpretation. Objective: (6.3) Use Law of Large Numbers

B

Melissa tosses a fair coin 4 times. What can we reasonably conclude about the outcome of 4 heads occurring? a. It will occur exactly one time. b. It will probably never occur, because it is an unusual outcome. c. It will occur exactly 4 times. d. None of the above is true. Objective: (6.3) Use Law of Large Number

D

Researchers as State University conducted experiments with a tomato plant. Listed below are the weights (in kilograms) of tomatoes given no treatment, and tomatoes treated with a fertilizer. Compare the variation in the two data sets. No treatment: 0.12 0.22 0.33 0.15 0.09 Fertilizer: 0.93 1.04 1.18 0.22 0.54 Fertilizer: 0.93 1.04 1.18 0.22 0.54

No treatment: range = 0.24 kg; standard deviation = 0.10 kg Fertilizer: range = 0.96 kg; standard deviation = 0.39 kg The tomatoes with no treatment appear to have weights that vary less than the weights of the fertilized tomatoes.

After recording delivery times for two different Chinese food restaurants, you concluded that one Chinese restaurant has a mean delivery time of 44 minutes with a standard deviation of 4 minutes and the other restaurant has a mean delivery time of 39 minutes with a standard deviation of 17 minutes. Interpret these figures. If you liked the Chinese food from both restaurants equally well, which one would you order from? Objective: (4.3) *Solve Apps: Compare Variation

Order from the first restaurant. The standard deviation is much lower.

You are a manager of a small factory that produces an electronic gadget. There is a day shift and a night shift working at the factory. The day shift produces gadgets with a mean defect rate of 4 defect per 1000 gadgets and a standard deviation of 3 defects per 1000 gadgets. The night shift produces gadgets with a mean defect rate of 2 defect per 1000 gadgets and a standard deviation of 10 defects per 1000 gadgets. Which shift is more likely to cause problems keeping defects down to quota on a single shift? Objective: (4.3) *Solve Apps: Compare Variation

The night shift, with a larger standard deviation, is more likely to cause a large amount of defects.

A study of two types of weed killers was done. One weed killer killed 35% more weeds than the other. This difference was significant at the 0.05 level. What does this mean? Objective: (6.1) Interpret Levels of Statistical Significance

The probability that one weed killer performed better by chance alone is less than a 0.05.

A study of 600 college students taking Statistics 101 revealed that 59 students received the grade of A. Typically 10% of the class gets an A. The difference between this group of students and the expected value is not significant at the 0.05 level. What does this mean in this case? Objective: (6.1) Interpret Levels of Statistical Significance

The probability that the difference occurred due to chance is more than 0.05.

Graph Question a .What is the mean of the distribution? b. Estimate the percentage of light bulbs having a life less than 3000 hours. c. Estimate (using area) the relative frequency of values between 2500 hours and 3000 hours.

a. 2500 b. 85 % c. 0.35

The table below gives the sale price of seven homes sold in the same neighborhood over a six-month period. Home (address) Price 100 Willow Dr. $303,000 215 Pebble Ln. $164,000 202 Driftwood St. $293,000 213 Lilac Dr. $313,000 154 Dogwood Dr. $491,000 303 Ash St. $280,000 222 Cedar Ln. $272,000 a. Find the mean price and median price for these homes. b. Which home is an outlier on the high end? If you eliminate this home, what are the new mean and median prices for these homes? c. Which home is an outlier on the low end? If you eliminate this home, what are the new mean and median prices for these homes? d. If you eliminate both outliers, what are the new mean and median prices for these homes? 1) Objective: (4.1) *Solve Apps:

a. Mean: $302,286; median: $293,000 b. 154 Dogwood Dr. is an outlier on the high end. Without 154 Dogwood Dr., the mean is $270,833 and the median is $286,500 c. 215 Pebble Ln. is an outlier on the low end. Without 215 Pebble Ln. (but with 154 Dogwood Dr.), the mean is $325,333 and the median is $298,000 d. Mean: $292,200; median: $293,000

9) Packages of a certain candy vary slightly in weight. Here are the measured weights of nine packages, in ounces: 1.7023 1.7044 1.7051 1.7066 1.6762 1.7048 1.7029 1.7035 1.7058 a. Find the mean and the median of these weights. b. Which, if any, of these weights would you consider to be an outlier? c. What are the mean and median weights of the outlier is excluded

a. Mean: 1.7013; median: 1.7044 b. 1.6762 is an outlier. c. Mean: 1.7044; median: 1.7046

The National Education Association collects data on the number of years of teaching experience of high-school teachers. A sample taken this year of 19 high-school teachers yielded the following data on number of years of teaching experience. 33 13 1 19 31 7 3 10 2 22 25 1 33 29 4 18 24 21 31 Objective: (4.3) Obtain Five-Number

low = 1, lower quartile = 4, median = 19, upper quartile = 29, high = 33

The weights (in pounds) of 18 randomly selected adults are given below. 120 146 187 153 119 138 127 141 179 163 182 202 114 171 131 149 169 171 24) Objective: (4.3) Obtain Five-Number Summary

low = 114, lower quartile = 131, median = 151.0, upper quartile = 171, high = 202

The test scores of 15 students are listed below. 42 46 48 55 57 60 66 68 72 79 85 87 90 94 95 Objective: (4.3) Obtain Five-Number Summary

low = 42, lower quartile = 55, median = 68, upper quartile = 87, high = 95

The weekly salaries (in dollars) of sixteen government workers are listed below. 690 592 813 653 728 572 492 618 525 659 685 472 561 787 511 826 Objective: (4.3) Obtain Five-Number Summary

low = 472, lower quartile = 543.0, median = 635.5, upper quartile = 709, high = 826