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mathematics
statistics

Questions and Answers of Statistics

Refer to Exercise.In exercise, barrick Gold (ABX), Bombardier (BBD.B), Bell Canada Enterprises (BCE), Bank of Montreal (BMO), Bank of Nova Scotia (BNS), Canadian Imperial Bank of Commerce (CM),
a. Bed Bath & Beyond (BBBY) (25%), Expedia (EXPE) (25%), Mattel (MAT) (25%), Starbucks (SBUX) (25%)b. BBBY (40%), EXPE (30%), MAT (20%), SBUX (10%)c. BBBY (10%), EXPE (20%), MAT (30%), SBUX (40%)d.
a. Netflix (NFLX) (25%), ScanDisk (SNDK) (25%), Sirius XM Radio (SIRI) (25%), Wynn Resorts (WYNN) (25%)b. NFLX (15%), SNDK (15%), SIRI (15%), WYNN (55%)c. NFLX (20%), SNDK (20%), SIRI (50%), WYNN
a. Amazon (AMZN) (25%), Apple (AAPL) (25%), Dell (DELL) (25%), Dollar Tree (DLTR) (25%)b. AMZN (10%), AAPL (20%), DELL (30%), DLTR (40%)c. AMZN (40%), AAPL (40%), DELL (10%), DLTR (10%)d. Which
Refer to Exercise.In Exercise, we calculated the returns on the following selected stocks on the NASDAQ Exchange for the period January 2008 to December 2012: Adobe Systems (ADBE), Amazon (AMZN),
In the game of roulette, a steel ball is rolled onto a wheel that contains 18 red, 18 black, and 2 green slots. If the ball is rolled 25 times, find the probabilities of the following events.a. The
Advertising researchers have developed a theory that states that commercials that appear in violent television shows are less likely to be remembered and will thus be less effective. After examining
Refer to Exercise 7.22.a. Determine the probability distribution of the amount of money the arcade takes in per child.b. Use the probability distribution to calculate the mean and variance of the
In Case, we presented the probabilities of scoring at least one run and asked you to determine whether the manager should signal for the batter to sacrifice bunt. The decision was made on the basis
Refer to Example 3.2. From the histogram for investment A, estimate the following probabilities.a. P(X > 45)b. P(10 < X < 40)c. P(X < 25)d. P(35 < X < 65)
Refer to Example 3.2. Estimate the following from the histogram of the returns on investment B.a. P(X > 45)b. P(10 < X < 40)c. P(X < 25)d. P(35 < X < 65)
Refer to Example 3.3. From the histogram of the marks, estimate the following probabilities.a. P(55 < X < 80)b. P(X > 65)c. P(X < 85)d. P(75 < X < 85)
A random variable is uniformly distributed between 5 and 25.a. Draw the density function.b. Find P(X > 25).c. Find P(10 < X < 15).d. Find P(5.0 < X < 5.1).
A uniformly distributed random variable has minimum and maximum values of 20 and 60, respectively.a. Draw the density function.b. Determine P(35 < X < 45).c. Draw the density function including
The amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 30 and 60 minutes. One student is selected at random. Find the probability of the following
The weekly output of a steel mill is a uniformly distributed random variable that lies between 110 and 175 metric tons.a. Compute the probability that the steel mill will produce more than 150 metric
Refer to Exercise 8.9. The operations manager labels any week that is in the bottom 20% of production a “bad week.” How many metric tons should be used to define a bad week?
A random variable has the following density function.f(x) = 1 − .5x 0 < x < 2a. Graph the density function.b. Verify that f(x) is a density function.c. Find P(X > 1).d. Find P(X < .5).e. Find P(X =
The following function is the density function for the random variable X:a. Graph the density function.b. Find the probability that X lies between 2 and 4.c. What is the probability that X is less
The following is a graph of a density function.a. Determine the density function.b. Find the probability that X is greater than 10.c. Find the probability that X lies between 6 and12.
X is normally distributed with mean 100 and standard deviation 20. What is the probability that X is greater than 145?
X is normally distributed with mean 250 and standard deviation 40. What value of X does only the top 15% exceed?
X is normally distributed with mean 1,000 and standard deviation 250. What is the probability that X lies between 800 and 1, 100?
X is normally distributed with mean 50 and standard deviation 8. What value of X is such that only 8% of values are below it?
The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes.Find the probability that a calla. Lasts between
Refer to Exercise 8.38. How long do the longest 10% of calls last?The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard
The lifetimes of light bulbs that are advertised to last for 5,000 hours are normally distributed with a mean of 5,100 hours and a standard deviation of 200 hours. What is the probability that a bulb
Refer to Exercise 8.40. If we wanted to be sure that 98% of all bulbs last longer than the advertised figure, what figure should be advertised?
Travelbyus is an Internet-based travel agency wherein customers can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of
Refer to Exercise 8.42. Some Internet sites have bandwidths that are not sufficient to handle all their traffic, often causing their systems to crash.Bandwidth can be measured by the number of hits a
A new gas–electric hybrid car has recently hit the market. The distance traveled on 1 gallon of fuel is normally distributed with a mean of 65 miles and a standard deviation of 4 miles. Find the
The top-selling Red and Voss tire is rated 70,000 miles, which means nothing. In fact, the distance the tires can run until they wear out is a normally distributed random variable with a mean of
The heights of 2-year-old children are normally distributed with a mean of 32 inches and a standard deviation of 1.5 inches. Pediatricians regularly measure the heights of toddlers to determine
Refer to Exercise 8.46. Find the probability of these events.a. A 2-year-old child is taller than 36 inches.b. A 2-year-old child is shorter than 34 inches.c. A 2-year-old child is between 30 and 33
University and college students average 7.2 hours of sleep per night, with a standard deviation of 40 minutes. If the amount of sleep is normally distributed, what proportion of university and
Refer to Exercise. Find the amount of sleep that is exceeded by only 25% of students.In Exercise, University and college students average 7.2 hours of sleep per night, with a standard deviation of 40
The amount of time devoted to studying statistics each week by students who achieve a grade of A in the course is a normally distributed random variable with a mean of 7.5 hours and a standard
The number of pages printed before replacing the cartridge in a laser printer is normally distributed with a mean of 11,500 pages and a standard deviation of 800 pages. A new cartridge has just been
Refer to Exercise 8.51. The manufacturer wants to provide guidelines to potential customers advising them of the minimum number of pages they can expect from each cartridge. How many pages should it
Battery manufacturers compete on the basis of the amount of time their products last in cameras and toys. A manufacturer of alkaline batteries has observed that its batteries last for an average of
Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid
It is said that sufferers of a cold virus experience symptoms for 7 days. However, the amount of time is actually a normally distributed random variable whose mean is 7.5 days and whose standard
How much money does a typical family of four spend at a McDonald’s restaurant per visit? The amount is a normally distributed random variable with a mean of $16.40 and a standard deviation of
The final marks in a statistics course are normally distributed with a mean of 70 and a standard deviation of 10. The professor must convert all marks to letter grades. She decides that she wants 10%
Mensa is an organization whose members possess IQs that are in the top 2% of the population. It is known that IQs are normally distributed with a mean of 100 and a standard deviation of 16. Find the
According to the 2001 Canadian census, university-educated Canadians earned a mean income of $61,823. The standard deviation is $17,301. If incomes are normally distributed, what is the probability
The census referred to in the previous exercise also reported that college-educated Canadians earn on average $41,825. Suppose that incomes are normally distributed with a standard deviation of
The lifetimes of televisions produced by the Hishobi Company are normally distributed with a mean of 75 months and a standard deviation of 8 months. If the manufacturer wants to have to replace only
According to the Statistical Abstract of the United States, 2012 (Table 721), the mean family net worth of families whose head is between 35 and 44 years old is approximately $325,600. If family net
A retailer of computing products sells a variety of computer-related products. One of his most popular products is an HP laser printer. The average weekly demand is 200. Lead time for a new order
The demand for a daily newspaper at a newsstand at a busy intersection is known to be normally distributed with a mean of 150 and a standard deviation of 25. How many newspapers should the news stand
Every day a bakery prepares its famous marble rye. A statistically savvy customer determined that daily demand is normally distributed with a mean of 850 and a standard deviation of 90. How many
Refer to Exercise 8.65. Any marble ryes that are unsold at the end of the day are marked down and sold for half-price. How many loaves should the bakery prepare so that the proportion of days that
Refer to Exercise 7.57. Find the probability that the project will take more than 60 days to complete.
The mean and variance of the time to complete the project in Exercise 7.58 was 145 minutes and 31 minutes2. What is the probability that it will take less than 2.5 hours to overhaul the
The annual rate of return on a mutual fund is normally distributed with a mean of 14% and a standard deviation of 18%.a. What is the probability that the fund returns more than 25% next year?b. What
In Exercise 7.64, we discovered that the expected return is .1060 and the standard deviation is .1456. Working with the assumption that returns are normally distributed, determine the probability of
Let X be an exponential random variable with λ = .5. Find the following probabilities.a. P(X > 1)b. P(X > .4)c. P(X < .5)d. P(X < 2)
X is an exponential random variable with λ = .3. Find the following probabilities.a. P(X > 2)b. P(X < 4)c. P(1 < X < 2)d. P(X = 3)
The production of a complex chemical needed for anticancer drugs is exponentially distributed with λ = 6 kilograms per hour. What is the probability that the production process requires more than
The time between breakdowns of aging machines is known to be exponentially distributed with a mean of 25 hours. The machine has just been repaired. Determine the probability that the next breakdown
When trucks arrive at the Ambassador Bridge, each truck must be checked by customs agents. The times are exponentially distributed with a service rate of 10 per hour. What is the probability that a
A bank wishing to increase its customer base advertises that it has the fastest service and that virtually all of its customers are served in less than 10 minutes. A management scientist has studied
Toll booths on the New York State Thruway are often congested because of the large number of cars waiting to pay. A consultant working for the state concluded that if service times are measured from
The manager of a gas station has observed that the times required by drivers to fill their car’s tank and pay are quite variable. In fact, the times are exponentially distributed with a mean of 7.5
Because automatic banking machine (ABM) customers can perform a number of transactions, the times to complete them can be quite variable. A banking consultant has noted that the times are
The manager of a supermarket tracked the amount of time needed for customers to be served by the cashier. After checking with his statistics professor, he concluded that the checkout times are
Use the t table (Table 4) to find the following values of t.a. t.10, 15b. t.10, 23c. t.025, 83d. t.05, 195
Use the t table (Table 4) to find the following values of t.a. t.005, 33b. t.10, 600c. t.05, 4d. t.01, 20
Use a computer to find the following values of t.a. t.10, 15b. t.10, 23c. t.025, 83d. t.05, 195
Use a computer to find the following values of t.a. t.05, 143b. t.01, 12c. t.025, ∞d. t.05, 100
Use a computer to find the following probabilities.a. P(t64 > 2.12)b. P(t27 > 1.90)c. P(t159 > 1.33)d. P(t550 > 1.85)
Use a computer to find the following probabilities.a. P(t141 > .94)b. P(t421 > 2.00)c. P(t1000 > 1.96)d. P(t82 > 1.96)
Use the χ2 table (Table 5) to find the following values of χ2.a. χ2.10, 5b. χ2.01, 100c. χ2.95, 18d. χ2.99, 60
Use the χ2 table (Table 5) to find the following values of χ2.a. χ2.90, 26b. χ2.01, 30c. χ2.10, 1d. χ2.99, 80
Use a computer to find the following values of χ2.a. χ2.25, 66b. χ2.40, 100c. χ2.50, 17d. χ2.10, 17
Use a computer to find the following values of χ2.a. χ2.99, 55b. χ2.05, 800c. χ2.99, 43d. χ2.10, 233
Use a computer to find the following probabilities.a. P(χ273 > 80)b. P(χ2200 > 125)c. P(χ288 > 60)d. P(χ21000 > 450)
Use a computer to find the following probabilities.a. P(χ2250 > 250)b. P(χ236 > 25)c. P(χ2600 > 500)d. P(χ2120 > 100)
Use the F table (Table 6) to find the following values of F.a. F.05, 3, 7b. F.05, 7, 3c. F.025, 5, 20d. F.01, 12,60
Use the F table (Table 6) to find the following values of F.a. F.025, 8, 22b. F.05, 20, 30c. F.01, 9, 18d. F.025, 24,10
Use a computer to find the following values of F.a. F.05, 70, 70b. F.01, 45, 100c. F.025, 36, 50d. F.05, 500, 500
Use a computer to find the following values of F.a. F.01, 100, 150b. F.05, 25, 125c. F.01, 11, 33d. F.05, 300, 800
Use a computer to find the following probabilities.a. P(F7, 20 > 2.5)b. P(F18, 63 > 1.4)c. P(F34, 62 > 1.8)d. P(F200, 400 > 1.1)
The following function is the density function for the random variable X:a. Graph the density function.b. Find the probability that X lies between 1 and 3.c. What is the probability that X lies
The random variable X is exponentially distributed with λ = 3. Sketch the graph of the distribution of X by plotting and connecting the points representing f(x) for x = 0, .5, 1, 1.5, and 2.
X is an exponential random variable with λ = .25. Sketch the graph of the distribution of X by plotting and connecting the points representing f(x) for x = 0, 2, 4, 6, 8, 10, 15, 20.
Use a computer to find the following probabilities.a. P(F600, 800 > 1.1)b. P(F35, 100 > 1.3)c. P(F66, 148 > 2.1)d. P(F17, 37 > 2.8)
Let x̄ represents the mean of the toss of two fair dice. Use the probabilities listed in Table to determine the following probabilities.xP(x)1.0 .............1/361.5 .............2/362.0
An experiment consists of tossing five balanced dice. Find the following probabilities.a. P(x̄ = 1)b. P(x̄ = 6)
Repeat Exercise 9.7 with n = 100.In Exercise A sample of n = 16 observations is drawn from a normal population with µ = 1,000 and σ = 200. Find the following.a. P (x̄ > 1,050)b. P (x̄ <
Given a normal population whose mean is 50 and whose standard deviation is 5, find the probability that a random sample ofa. 4 have a mean between 49 and 52.b. 16 have a mean between 49 and 52.c. 25
Repeat Exercise 9.10 for a standard deviation of 10.In Exercise Given a normal population whose mean is 50 and whose standard deviation is 5, find the probability that a random sample ofa. 4 have a
Repeat Exercise for a standard deviation of 20.In Exercise, given a normal population whose mean is 50 and whose standard deviation is 5, find the probability that a random sample ofa. 4 have a mean
a. Calculate the finite population correction factor when the population size is N = 1,000 and the sample size is n = 100.b. Repeat part (a) when N = 3,000.c. Repeat part (a) when N = 5,000.d. What
a. Suppose that the standard deviation of a population with N = 10,000 members is 500. Determine the standard error of the sampling distribution of the mean when the sample size is 1,000.b. Repeat
The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches.a. What is the probability that a randomly selected woman is taller than 66
An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean = 117 cm and standard deviation = 5.2 cm.a. Find
The amount of time the university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours.a. What is the probability that a
The number of pizzas consumed per month by university students is normally distributed with a mean of 10 and a standard deviation of 3.a. What proportion of students consumes more than 12 pizzas per

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