Question: What does it mean when we write

> Estimate the death rate for 60-year-olds. If the population of people this age is about 14 million, how many people of this age can be expected to die in a year? Figure 6.13 (a) The overall U.S. death rate (deaths per 1000 people) for different ages.

> Refer again to the scatterplot in Figure 7.24. Does there appear to be a significant correlation between the two variables? Figure 7.24.

> If you lived in a typical city of 500,000, how many people would you expect to die due to chronic respiratory diseases in a year? Source: Centers for Disease Control and Prevention; data for 2014.

> If you lived in a typical city of 500,000, how many people would you expect to die due to a stroke in a year?

> What is the death rate due to heart disease in deaths per 100,000 of the population? Source: Centers for Disease Control and Prevention; data for 2014.

> What is the death rate due to Alzheimer’s disease in deaths per 100,000 of the population? Source: Centers for Disease Control and Prevention; data for 2014.

> Find the death rate of 20-year-olds per 100,000 people during the year. How many 20-year-olds would be expected to die out of 10,000 people?

> Find the death rate of 19-year-olds per 100,000 people during the year. How many 19-year-olds would be expected to die out of 10,000 people?

> Based on current life expectancy data, how many years is a randomly selected 18-year-old expected to live beyond his or her 18th birthday?

> Based on current life expectancy data, how many years is a randomly selected 20-year-old expected to live beyond his or her 20th birthday?

> Compare the death rates per 1000 people for California and the United States.

> Compare the death rates per 1000 people for California and Florida. Identify a reason for the difference.

> Estimate the correlation coefficient for the data points in the scatterplot in Figure 7.24. Figure 7.24.

> Find the birth rate per 1000 people for California.

> Find the birth rate per 1000 people for the United States.

> For the year 2014, find the fatality rate in deaths per passenger mile (instead of per billion passenger miles). Why don’t we report the fatality rate in units of deaths per passenger mile?

> For each of the three years, find the fatality rate in deaths per million passengers. On the basis of those rates, which year was the safest? Why?

> For each of the three years, find the fatality rate in deaths per billion passenger miles. On the basis of those rates, which year was the safest? Why?

> For each of the three years, find the fatality rate in deaths per 1000 departures. On the basis of those rates, which year was the safest? Why?

> A 60-year-old has a shorter life expectancy than a 20-year-old.

> Your life expectancy is the major factor in determining how long you live.

> The death rate for motorcycle accidents is much higher than the death rate for automobile accidents, so more people must die in motorcycle accidents than in car accidents.

> What is the gambler’s fallacy? Give an example.

> For a collection of 50 pairs of sample data values, the correlation coefficient is found to be r  -0.900. Which of the following statements best describes the relationship between the two variables? a. There is no correlation. b. There is a weak positiv

> What is an expected value, and how is it computed? Should we always expect to realize the expected value? Why or why not?

> In terms of the law of large numbers, explain why you should not be surprised to see 6 heads in 10 tosses of a fair coin, but you should be surprised to see 600 heads in 1000 tosses of the same coin.

> What is the law of large numbers? Can it be applied to a single observation or experiment? Explain.

> Can You Catch Up? Suppose that you toss a fair coin 100 times, getting 38 heads and 62 tails, which is 24 more tails than heads. a. Explain why, on your next toss, the difference in the numbers of heads and tails is as likely to grow to 25 as it is to sh

> In 1953, a French economist named Maurice Allais conducted a survey of how people assess risk. Here are two scenarios that he used, each of which required people to choose between two options. Decision 1 Option A: 100% chance of gaining $1,000,000 Optio

> Reader’s Digest ran a sweepstakes in which prizes were listed along with the chances of winning: $1,000,000 (1 chance in 90,000,000), $100,000 (1 chance in 110,000,000), $25,000 (1 chance in 110,000,000), $5,000 (1 chance in 36,667,000), and $2,500 (1 ch

> Football teams have the option of trying to score either 1 or 2 extra points after a touchdown. A team scores 1 point by kicking the ball through the goal posts or 2 points by running or passing the ball across the goal line. For a recent year in the NFL

> In New Jersey’s Pick 4 lottery, you pay 50¢ to select a sequence of four digits, such as 2273, from the 10,000 different possible four-digit sequences. If you select the same sequence of four digits that are drawn, you win and collect $2788. What is your

> When you give a casino $20 for a bet on the “pass line” in a dice game, there is a 251/495 probability that you will lose $20 and there is a 244/495 probability that you will make a net gain of $20. (If you win, the casino gives you $20 and you get to ke

> As shown in Figure 6.11, a roulette wheel has 38 numbers, with 18 odd numbers (black) and 18 even numbers (red), as well as 0 and 00 (which are green). If you bet $5 that the outcome is an odd number, the probability of losing the $5 is 20/38 and the pro

> Which of the following are likely to have a correlation? a. Amounts donated to charities in a year and annual incomes. b. Hat sizes and annual incomes of randomly selected adults. c. Braking reaction times and weights of randomly selected adults. d. Heig

> You arrive at a bus stop randomly, and all arrival times are equally likely. The bus arrives regularly every 24 minutes without delay. What is the expected value for your waiting time?

> There is a 0.9968 probability that a randomly selected 50-year-old female will live through the year. A life insurance company charges $226 for insuring that the female will live through the year. If she does not survive the year, the policy pays out $50

> There is a 0.9986 probability that a randomly selected 30-year-old male will live through the year. A life insurance company charges $161 for insuring that the male will live through the year. If he does not survive the year, the policy pays out $100,000

> If you bet $1 in Kentucky’s Pick 4 lottery, you either lose $1 or gain $4999. (The winning prize is $5000, but your $1 bet is not returned, so the net gain is $4999.) The game is played by selecting a four-digit number between 0000 and 9999. What is the

> Suppose you are offered this opportunity: You can place a bet of $10 and someone else tosses a coin. You win an additional $15 if heads occurs, and you lose your $10 if tails occurs. What is the expected value of this game? Should you play?

> A person who has a habit of driving fast has never had a traffic citation. What does it mean to say that “the law of averages will catch up with him”? Is it true? Explain.

> In analyzing genders of newborns, assume that boys and girls are equally likely. Among 500 births, should we expect exactly 250 boys and 250 girls? As the number of births increases, what does the law of large numbers tell us about the proportion of girl

> I haven’t won in my last 25 pulls on the slot machine, so I’m due to win on the next couple of pulls.

> For the California Daily 3 lottery, in which you pick three numbers, it is better to select the numbers 5-3-9 than the numbers 1-2-3, because 5-3-9 is more random.

> For a $1 “straight” bet in the California Daily 3 lottery, the expected return is 64¢, so betting a dollar for fun is okay, but it is unwise to bet much money on this lottery.

> If a best-fit line is inserted in a scatterplot, it must pass through every point on the graph.

> For a typical lottery, the expected value of a ticket is less than the cost of a ticket.

> What is a probability distribution? Briefly describe a format that is used to display a probability distribution.

> Briefly describe the theoretical, relative frequency, and subjective methods for finding probabilities. Give an example of each.

> Distinguish between an outcome and an event in probability. Give an example in which the same event can occur via two or more outcomes.

> The histogram in Figure 6.9 shows the distribution of “Mega” numbers (possible values range from 1 to 27) that were drawn in 1639 separate plays of the California lottery game Mega Millions. a. Assuming the lottery dra

> After constructing a table that is similar to Table 6.2 and shows all possible outcomes of tossing four coins at once, find the following. a. Find the probability that all four tosses are the same (all heads or all tails). b. Find the probability that th

> In a clinical trial in which 73 patients with carpal tunnel syndrome were treated with surgery, 67 had successful treatment (based on data from “Splinting vs. Surgery in the Treatment of Carpal Tunnel Syndrome” by Gerritsen et al., Journal of the America

> Halfway through the season, a basketball player has made 72% of her free throws. What is the probability that her next free throw will be successful?

> What is the probability of a 100-year flood happening this year?

> Every possible correlation coefficient must lie between the values of ____ and____.

> After recording the forecasts of your local meteorologist for 30 days, you conclude that she gave a correct forecast for 26 days. What is the probability that her next forecast will be correct?

> Suppose you randomly select a family with four children. Assume that births of boys and girls are equally likely. a. How many birth orders are possible? List them in a probability distribution table. b. What is the probability that the family has four ch

> Suppose you randomly select a family with three children. Assume that births of boys and girls are equally likely. a. How many birth orders are possible? List them in a probability distribution table. b. What is the probability of two boys and a girl? c.

> The New England College of Medicine uses an admissions test with many multiple-choice questions, each with five possible answers, only one of which is correct. If you guess randomly on every question, what score might you expect to get? (Express the answ

> A bag contains 13 red M&Ms, 25 orange M&Ms, 8 yellow M&Ms, 8 brown M&Ms, 27 blue M&Ms, and 19 green M&Ms. When randomly selecting one M&M, what is the probability of drawing a red M&M? A blue M&M? A yellow M&M? An M&M that is not orange?

> What is the probability of not buying a defective smart phone when quality control surveys indicate that 2% of all smart phones purchased are defective?

> What is the probability of randomly selecting a person and getting someone who does not have type O blood, given that 45% of people have type O blood?

> What is the probability of finding that the next President of the United States was not born on Saturday?

> What is the probability that a 75% free-throw shooter will miss her next free throw?

> What is the probability of randomly selecting a day of the week and not picking a day whose name includes the letter “t”?

> Find the probability of getting someone who failed the exam or was in Group A.

> A Las Vegas handicapper can correctly predict the winner in a professional basketball game 60% of the time. What is the probability that she is wrong in her next prediction?

> Refer to Figure 9.29. For the variables given, calculate and plot , u, and ’ with depth.

> Refer to Figure 9.29. For the variables given, calculate and plot , u, and ’ with depth.

> From the sieve analysis of a sand, the effective size was determined to be 0.18 mm. Using Hazen’s formula, Eq. (9.34), estimate the range of capillary rise in this sand for a void ratio of 0.65.

> Refer to Figure 9.26. Calculate , u, and ’ at A, B, C, and D for the following cases, and plot the variations with depth. (Note: e = void ratio,  = moisture content, Gs = specific

> Repeat Problem 8.8 using L. Casagrande’s method.

> An earth dam is shown in Figure 8.32. Determine the seepage rate, q, in m3 /day/m length. Given: a1 = 358, a2 = 408, L1 = 5 m, H = 7 m, H1 = 10 m, and k = 3 × 10-4 cm/s. Use Schaffernak’s solution.

> For the weir shown in Figure 8.31, calculate the seepage in the permeable layer in m3/day/m for x9 = 1 m and x9 = 2 m. Use Figure 8.13.

> Draw a flow net for the weir shown in Figure 8.30. Calculate the rate of seepage under the weir.

> Refer to Problem 8.4. Using the flow net drawn, calculate the hydraulic uplift force at the base of the hydraulic structure per meter length (measured along the axis of the structure).

> For the hydraulic structure shown in Figure 8.29, draw a flow net for flow through the permeable layer and calculate the seepage loss in m3 /day/m.

> The porosity of a soil is 0.35. Given Gs = 2.69, calculate: Saturated unit weight (kN/m3 ) Moisture content when moist unit weight 5 17.5 kN/m3

> Refer to Figure 8.28. Given: H1 = 4 m D1 = 6 m H2 = 1.5 m D = 3.6 m Calculate the seepage loss in m3/day per meter length of the sheet pile (at right angles to the cross section shown). Use Figure 8.12.

> Draw a flow net for the single row of sheet piles driven into a permeable layer as shown in Figure 8.28. Given: H1 = 3 m D = 1.5 m H2 = 0.5 m D1 = 3.75 m Calculate the seepage loss per meter length of the sheet pile (at right angles to the cross s

> An earth dam section is shown in Figure 8.33. Determine the rate of seepage through the earth dam using Pavlovsky’s solution. Use k = 4 × 10-5 mm/s.

> Solve Problem 8.10 using L. Casagrande’s method.

> Refer to the cross section of the earth dam shown in Figure 8.19. Calculate the rate of seepage through the dam (q in m3/min/m) using Schaffernak’s solution.

> Refer to Figure 8.28. Given: H1 = 6 m D = 3 m H2 = 1.5 m D1 = 6 m Draw a flow net. Calculate the seepage loss per meter length of the sheet pile (at a right angle to the cross section shown).

> Refer to Figure 7.31. Find the flow rate in m3 /s/m (at right angles to the cross section shown) through the permeable soil layer. Given: H = 5 m, H1 = 2.8 m; h = 3.1 m, L = 60 m,  = 5°, and k = 0.05 cm/s.

> A permeable layer is underlain by an impervious layer, as shown in Figure 7.30. With k = 5.2 ×10-4 cm/s for the permeable layer, calculate the rate of seepage through it in m3 /hr/m if H = 3.8 m and α = 12°.

> A sand layer of the cross-sectional area shown in Figure 7.29 has been determined to exist for an 800 m length of the levee. The hydraulic conductivity of the sand layer is 2.8 m/day. Determine the quantity of water which flows into the ditch in m3 /min.

> For a falling-head permeability test, the following are given: Length of the soil specimen = 700 mm Area of the soil specimen = 20 cm2 Area of the standpipe = 1.05 cm2 Head difference at time t = 0 is 800 mm Head difference at time t = 8 min is 500 mm De

> A hydrometer test has the following results: Gs = 2.6, temperature of water = 24°C, and R = 43 at 60 minutes after the start of sedimentation (see Figure 2.30). What is the diameter D of the smallest-size particles that have settled beyond the zone of me

> For a falling-head permeability test, the following are given: length of specimen = 380 mm; area of specimen = 6.5 cm2; k = 0.175 cm/min. What should the area of the standpipe be for the head to drop from 650 cm to 300 cm in 8 min?

> For a falling-head permeability test, the following are given: Length of the soil specimen = 500 mm Area of the soil specimen = 26 cm2 Area of the standpipe = 1.3 cm2 Head difference at time t = 0 is 760 mm Head difference at time t = 10 min is 300 mm De

> In a constant-head permeability test in the laboratory, the following are given: L = 305 mm and A = 95 cm2. If the value of k = 0.015 cm/s and a flow rate of 7300 cm3/hr must be maintained through the soil, what is the head difference, h, across the spec

> Refer to Figure 7.5. For a constant-head permeability test in a sand, the following are given: L = 300 mm A = 175 cm2 h = 500 mm Water collected in 3 min = 620 cm3 Void ratio of sand = 0.58 Determine: Hydraulic conductivity, k (cm/s) Seepage veloc

> Consider the setup shown in Figure 7.34 in which three different soil layers, each 200 mm in length, are located inside a cylindrical tube of diameter 150 mm. A constant-head difference of 470 mm is maintained across the soil sample. The porosities and h

> A layered soil is shown in Figure 7.33. Estimate the ratio of equivalent hydraulic conductivity, kH(eq)/kV(eq).

> A layered soil is shown in Figure 7.32. Given: H1 = 1.5 m k1 = 10-5 cm/s H2 = 2.5 m k2 = 3.0 × 10-3 cm/s H3 = 3.0 m k3 = 3.5 × 10-5 cm/s Estimate the ratio of equivalent permeability, kH(eq)/kV(eq).

> The in situ void ratio of a soft clay deposit is 2.1, and the hydraulic conductivity of the clay at this void ratio is 0.91 ×10-6 cm/s. What is the hydraulic conductivity if the soil is compressed to have a void ratio of 1.1? Use Eq. (7.34).

> For a normally consolidated clay, the following are given: Estimate the hydraulic conductivity at a void ratio e = 0.9. Use Eq. (7.36).

> The sieve analysis for a sand is given in the following table. Estimate the hydraulic conductivity of the sand at a void ratio of 0.5. Use Eq. (7.30) and SF =6.5