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mathematics
calculus

Questions and Answers of Calculus

Suppose 4 rats are placed in a T-maze in which they must turn right or left. If each rat makes a choice by chance, what is the probability that 2 of the rats will turn to the right?
A baseball player has a lifetime batting average of 0.300. If he comes to bat 5 times in a given game, what is the probability that (a) He will get 3 hits? (b) He will get more than 3 hits?
A company produces shotgun shells in batches of 300. A sample of 10 is tested from each batch, and if more than one defect is found, the entire batch is tested. If 1% of the shells are actually
If the probability of success on each trial of an experiment is 0.3, what is the probability of 4 successes in 6 independent trials?
A baseball pitching machine throws a bad pitch with probability 0.1. What is the probability that the machine will throw 5 or fewer bad pitches out of 20 pitches?
A quiz consists of 10 multiple-choice questions with 5 choices for each question. Suppose a student is sure of the first 5 answers and has each of the last 5 questions narrowed to 3 of the possible 5
1. In a certain community, 10% of the population is Jewish. A study shows that of 7 social service agencies, 4 have board presidents who are Jewish. Find the probability that this could happen by
If the probability of success on each trial of an experiment is 0.4, what is the probability of 5 successes in 8 trials?
Suppose a fair coin is tossed 6 times. What is the probability that (a) 6 heads will occur? (b) 3 heads will occur? (c) 2 heads will occur?
If a fair die is rolled 3 times, what is the probability that (a) A 5 will result 2 times out of the 3 rolls? (b) An odd number will result 2 times? (c) A number divisible by 3 will occur 3 times?
Suppose a fair die is rolled 12 times. What is the probability that 5 "aces" (1s) will occur?
In Problem 7, what is the probability that no aces will occur? Suppose a fair die is rolled 12 times. What is the probability that 5 "aces" (1s) will occur?
A bag contains 6 red balls and 4 black balls. We draw 5 balls, with each one replaced before the next is drawn. (a) What is the probability that 2 balls drawn will be red? (b) What is the probability
Construct frequency histograms for the data given in the frequency tables.1.Score
Find the medians of the sets of scores. 1. 1, 3, 6, 7, 5 2. 2, 1, 3, 4, 2, 1, 2 3. 4, 7, 9, 18, 36, 14, 3, 12 4. 1, 0, 2, 1, 1, 0, 2, 14, 37
Find the modes, medians, and means of the scores.1. 3, 2, 1, 6, 8, 12, 14, 22. 5, 8, 7, 6, 1, 1, 313. 14, 17, 20, 31, 17, 42
Use class marks to find the mean, mode, and median of the data in Problem 5. Interval
Use class marks to find the mean, mode, and median of the data in Problem 6. Interval
Find the range of the set of numbers given. 1. 3, 5, 7, 8, 2, 11, 6, 5 2. 5, 1, 3, 1.4, 6.3, 8 3. - 1, 2, 4, 3, 6, 11, 3, 4, 2 4. 2, 3, 3, 3, 3, 3, 9
Find the mean, variance, and standard deviation of each of the sets of sample data.1. 5, 7, 1, 3, 0, 8, 6, 22. 7, 13, 5, 11, 8, 10, 93. 11, 12, 13, 14, 15, 16, 174. 4, 3, 6, 7, 8, 9, 12
Find the mean and standard deviation of the sample data in each table.1.2.
The table gives the U.S. unemployment rates for civilian workers for selected years 1960-2013.(a) Display these data with a bar graph.(b) Summarize the data by finding the mean and standard deviation
The population (in millions) of Americans under the age of 18 for years from 2016 and projected through 2050 is shown in the table. Construct a bar graph of the population for the given time
The table summarizes the number of mobile phones per 100 people in the population of each of the countries with at least 100 mobile phones per 100 people. Construct a frequency histogram of the
A taxi company tests a new brand of tires by putting a set of four on each of three taxis. The table indicates the numbers of miles the tires lasted. Display these data with a histogram and find the
Suppose you live in a neighborhood with a few expensive homes and many modest homes. 1. If you wanted to impress people with the neighborhood where you lived, which measure would you give as the
1. The following table gives projections for 2062 of the percent of energy that will be renewable in the top five world regions. (a) Find the mean and standard deviation of the data. (b) Does the
The percents of total households that have married couples for selected years 1982 to 2012 are given in the table. Construct a frequency histogram of the percents.
The table gives the average retail prices for unleaded regular gasoline in U.S. cities for the years 1989-2013. Construct a frequency histogram of the gasoline prices, using intervals of 50 cents,
The birth weights (in kilograms) of a sample of 160 children are given in the table. Find the mean and standard deviation of the weights.
S & S Printing has 15 employees and 5 job classifications. Positions and wages for these employees are given in the table.(a) What is the mean salary per job classification? (b) What is the mean
Suppose a company has 10 employees, 1 earning $160,000, 1 earning $120,000, 2 earning $60,000, 1 earning $40,000, and 5 earning $32,000.(i). What is the mean salary for the company?(ii). What is the
Suppose a company has 10 employees, 1 earning $160,000, 1 earning $120,000, 2 earning $60,000, 1 earning $40,000, and 5 earning $32,000.(a) What is the mean salary for the company?(b) What is the
Suppose a company has 10 employees, 1 earning $160,000, 1 earning $120,000, 2 earning $60,000, 1 earning $40,000, and 5 earning $32,000.(a) What is the mean salary for the company?(b) What is the
A new car with a $38,000 list price can be bought for different prices from different dealers. In one city the car can be bought for $36,400 from 2 dealers, for $36,000 from 1 dealer, for $35,600
A new car with a $38,000 list price can be bought for different prices from different dealers. In one city the car can be bought for $36,400 from 2 dealers, for $36,000 from 1 dealer, for $35,600
The table gives the monthly insurance rates for a $100,000 life insurance policy for smokers aged 35-49.(a) Find the mean monthly insurance rate for these ages.(b) Find the standard deviation of the
The population (in millions) of Americans under the age of 18 for selected years from 2015 and projected through 2060 is shown in the following table.(a) Find the mean of this population over this
1. The following table gives the enrollments in U.S. public schools, in thousands, for selected years from 1899 and projected to 2022.(a) What is the mean public school enrollment for these years?(b)
The data in the table give the total numbers of prisoners executed in the United States from 1984 to 2013.(a) Construct a bar graph with x as the years (in groups of 5) and with f(x) as the number of
Construct frequency histograms for the data. 1. 3, 2, 5, 6, 3, 2, 6, 5, 4, 2, 1, 6 2. 5, 4, 6, 5, 4, 6, 3, 6, 5, 4, 1, 7
Find the modes of the sets of scores. 1. 3, 4, 3, 2, 2, 3, 5, 7, 6, 2, 3 2. 5, 8, 10, 12, 5, 4, 6, 3, 5 3. 14, 17, 13, 16, 15, 12, 13, 12, 13 4. 5, 7, 7, 7, 9, 12, 4, 6, 6, 8
Determine whether each table describes a discrete probability distribution. Explain. 1. x Pr(x) 1.........................-
Find the mean, variance, and standard deviation for each probability distribution. 1. x Pr(x) 0...................1/4 1...................1/4 2...................1/8 3...................3/8 2. x
Suppose an experiment has five possible outcomes for x: 0, 1, 2, 3, 4. The probability that each of these outcomes occurs is x/10. What is the expected value of x for the experiment?
Suppose an experiment has six possible outcomes for x: 0, 1, 2, 3, 4, 5. The probability that each of these outcomes occurs is x/15. What is the expected value of x for the experiment?
Five slips of paper containing the numbers 0, 1, 2, 3, 4 are placed in a hat. If the experiment consists of drawing one number, and if the experiment is repeated a large number of times, what is the
An experiment consists of rolling a die once. If the experiment is repeated a large number of times, what is the expected value of the number rolled?
A die is rolled 3 times, and success is rolling a 5. (a) Construct the binomial distribution that describes this experiment. (b) Find the mean of this distribution. (c) Find the standard deviation of
A die is rolled 3 times. Success is rolling a number divisible by 3. (a) Construct the binomial distribution that describes this experiment. (b) Find the mean of this distribution. (c) Find the
1. A variable x has a binomial distribution with probability of success 0.7 for each trial. For a total of 60 trials, what are (a) The mean and (b) The standard deviation of the distribution? 2. A
A coin is "loaded" so that the probability of tossing a head is 3/5. If it is tossed 50 times, what are (a) The mean and (b) The standard deviation of the number of heads that occur?
1. Suppose a pair of dice is thrown 1200 times. How many times would we expect a sum of 7 to occur? 2. Suppose a pair of dice is thrown 900 times. How many times would we expect a sum of 6 to
1. Expand (a + b)6.2. Expand (x + y)5.3. Expand (x + h)4.
Write the general expression for (x + h)n.
1. In studying endangered species, scientists have found that when animals are relocated, it takes x years without offspring before the first young are born, where x and the probability of x are
A candidate must decide whether he should spend his time and money on TV commercials or making personal appearances. His staff determines that by using TV he can reach 100,000 people with probability
If the probability that a newborn child is a male is 1/2, what is the expected number of male children in a family having 4 children?
A nonprofit organization sells chances for a $40,000 classic Mustang at $100 per ticket. It sells Expected loss $67.331500 tickets and offers four prizes, summarized in the table. What are the
1. A charity sells raffle tickets for $1 each. First prize is $500, second prize is $100, third prize is $10. If you bought one of the 1000 tickets sold, what are your expected winnings? 2. Suppose a
A young man plans to sell umbrellas at the city's Easter Parade. He knows that he can sell 180 umbrellas at $10 each if it rains hard, he can sell 50 if it rains lightly, and he can sell 10 if it
A candidate must decide whether he should spend his advertising dollars on print advertising or on telemarketing. His staff determines that by using print advertising he can reach 80,000 people with
A car owner must decide whether she should take out a $100-deductible collision policy in addition to her liability insurance policy. Records show that each year, in her area, 8% of the drivers have
Suppose a company manufactures altimeters so that they are accurate at an average height of 1000 feet. Is the accuracy of this single measurement sufficient to ensure the safety of the passengers and
A machinist makes pipes with an average diameter of 2 inches. If he machines 100 pipes with an average diameter of 2 inches, does this mean that all of them are usable? (A pipe is usable if its
Suppose that 10% of the patients who have a certain disease will die from it. (a) If 100 people have the disease, how many would we expect to die from it? (b) What is the standard deviation of the
A candidate claims that 60% of the voters in his district will vote for him. (a) If his district contains 100,000 voters, how many votes does he expect to get from his district? (b) What is the
Determine whether each formula describes a discrete probability distribution. Explain. 1. Pr(x) = x/21; x = 0, 1, 2, 3, 4, 5, 6 2. Pr(x) = x/10; x = 1, 2, 3, 4 3. Pr(x) = 10-x/10; x = 1, 2, 3, 4,
In a family with 2 children, the probability that both children will be boys is 1/4. (a) If 1200 families with two children are selected at random, how many of the families would we expect to have 2
If the number of votes the candidate in Problem 49 gets is 2 standard deviations below what he expected, how many votes will he get (approximately)?
A multiple-choice test has 20 questions and 5 choices for each question. If a student is totally unprepared and guesses on each question, the mean is the number of questions she can expect to answer
A certain calculator circuit board is manufactured in lots of 200. If 1% of the boards are defective, find the mean and standard deviation of the number of defects in each lot.
A certain type of corn seed has an 85% germination rate. If 2000 seeds were planted, how many seeds would be expected not to germinate?
Defines a discrete probability distribution. Find the expected value of each distribution.1.2. 3. 4.
Use Appendix C to find the probability that a z-score from the standard normal distribution will lie within each of the intervals. 1. 0 ≤ z ≤ 1.8 2. 0 ≤ z ≤ 2.4 3. - 0.6 ≤ z ≤ 0 4. -3 ≤
Suppose a population of scores x is normally distributed with μ = 20 and σ = 5. Use the standard normal distribution to find the probabilities indicated. 1. Pr(20 ≤ x ≤ 22.5) 2. Pr(20 ≤ x ≤
Suppose a population of scores x is normally distributed with μ = 50 and σ = 10. Use the standard normal distribution to find the probabilities indicated. 1. Pr(45 ≤ x ≤ 55) 2. Pr(42 ≤ x ≤
Suppose a population of scores x is normally distributed with μ = 110 and σ = 12. Use the standard normal distribution to find the probabilities indicated. 1. Pr(x < 134) 2. Pr(x < 88) 3. Pr(x >
Find the number A that satisfies Pr(z > A) = 0.95 for the standard normal z-score.
Find the number A that satisfies Pr(- A < z< A)= 0.8664 for the standard normal z-score.
The random variable x has a normal distribution with μ = 3 and σ = 4. Find B so Pr(x < B) = 0.75
The random variable x has a normal distribution with μ = 40 and σ = 5. Find B so Pr(x > B) = 0.12
The Fish Commission states that the lengths of all fish in Spring Run are normally distributed, with mean μ = 15 cm and standard deviation σ = 4 cm. What is the probability that a fish caught in
A quart of Parker's milk contains a mean of 39 grams of butterfat, with a standard deviation of 2 grams. If the butterfat is normally distributed, find the probability that a quart of this brand of
The heights of a certain species of plant are normally distributed, with mean μ = 20 cm and standard deviation σ = 4 cm. What is the probability that a plant chosen at random will be between 10 and
The durations of the mating calls of a population of tree toads are normally distributed, with mean 189 milliseconds (msec) and standard deviation 32 msec. What proportion of these calls would be
The mean weight of a group of boys is 160 lb, with a standard deviation of 15 lb. If the weights are normally distributed, find the probability that one of the boys picked at random from the group
The Scholastic Aptitude Test (SAT) scores in mathematics at a certain high school are normally distributed, with a mean of 500 and a standard deviation of 100. What is the probability that an
A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 28 mpg and a standard deviation of 4 mpg. Find the probability that a car selected
A machine precision-cuts tubing such that μ = 40.00 inches and σ = 0.03 inch. If the lengths are normally distributed, find the probability that a piece of tubing selected at random measures (a)
Systolic blood pressure for a group of women is normally distributed, with a mean of 120 and a standard deviation of 12. Find the probability that a woman selected at random has blood pressure (a)
In a certain state, the daily amounts of industrial waste are normally distributed, with a mean of 8000 tons and a standard deviation of 2000 tons. Find the probability that on a randomly selected
Reaction time is normally distributed, with a mean of 0.7 second and a standard deviation of 0.1 second. Find the probability that an individual selected at random has a reaction time (a) Greater
Suppose that the electrical supplies distributor in Example 6 wants to reduce its daily inventory but wants to limit to 5% the number of days that it will have an insufficient inventory of 48-in.
At a major university, exam scores, x, in a large enrollment course are normally distributed with a mean score of 78 and standard deviation of 6. If the test is curved so that the top 10% of scores
The amount spent monthly, x, for maintenance and repairs at XONIX, LLC, is normally distributed with a mean of $250 and standard deviation of $30. If x is the amount budgeted for next month, find x
The milk machine at a large dairy can be set to fill containers of various sizes. The fill-amounts are normally distributed with the mean equal to the fill amount setting and a standard deviation of
A textile manufacturer produces bolts of fabric with widths that are normally distributed with a mean of 48" and standard deviation of 0.25". Find the tolerance x so that 92% of the time the width of
At a certain college, GPAs are normally distributed with a mean GPA of 2.48 and a standard deviation of 0.9. If the college wants to limit the number of academic suspensions to at most 15% of its
Indicate which of the binomial distributions can be approximated by a normal distribution. 1. n = 28, p = 0.3 2. n = 45, p = 0.1 3. n = 12, p = 0.3 4. n = 200, p = 0.005

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