Questions and Answers of Essential Statistics

Lightbulbs: The lifetime of lightbulbs has a mean of 1500 hours and a standard deviation of 100 hours. A sample of 50 lightbulbs is tested.a. What is the probability that the sample mean lifetime is
Take your medicine: Medication used to treat a certain condition is administered by syringe. The target dose in a particular application is 10 milligrams. Because of the variations in the syringe, in
Your battery is dead: The lifetimes of a certain type of automobile battery are normally distributed with mean 5.9 years and standard deviation 0.4 year. The batteries are guaranteed to last at least
Find the z-score: Find the z-score for which the area to its right is 0.89.
Find the area: Find the area under the standard normal curvea. To the left of z = 0.35b. To the right of z = −1.56c. Between z = 0.35 and z = 2.47
Is it reasonable to treat the following sample as coming from an approximately normal population? Explain.5.5 8.7 9.3 10.1 15.2 3.5 11.9 7.6 13.7 8.7 14.3 5.8
Let X have a binomial distribution with n = 240 and p = 0.38. Use the normal approximation to find:a. P(X > 83)b. P(75 ≤ X ≤ 95)c. P(X < 96)
On a certain television channel, 18% of commercials are local advertisers. A sample of 120 commercials is selected.a. What is the probability that more than 20% of the commercials in the sample are
A sample of size n = 55 is drawn from a population with proportion p = 0.34. Let ̂p be the sample proportion.a. Find ????̂p and ????̂p.b. Find P( ̂p > 0.21).c. Find P( ̂p < 0.40).
The running time for videos submitted to YouTube in a given week is normally distributed with ???? = 390 seconds and standard deviation ???? = 148 seconds.a. If a single video is randomly selected,
Compute ????̄ x and ????̄ x for samples of size n = 64.
A population has mean ???? = 193 and standard deviation ???? =
State the Central Limit Theorem.
Suppose that in a bowling league, the scores among all bowlers are normally distributed with mean ???? = 182 points and standard deviation ???? = 14 points. A trophy is given to each player whose
A normal population has mean ???? = 242 and standard deviation ???? = 31.a. What proportion of the population is greater than 233?b. What is the probability that a randomly chosen value will be less
Suppose that salaries of recent graduates from a certain college are normally distributed with mean ???? = $42,650 and standard deviation ???? = $3800. What two salaries bound the middle 50%?
Find z0.15.
Find the z-scores that bound the middle 80% of the area under the normal curve.
Find the z-score that hasa. An area of 0.33 to its leftb. An area of 0.79 to its right
Find the area under the standard normal curvea. To the left of z = 1.77b. To the right of z = 0.41c. Between z = −2.12 and z = 1.37
Following is a probability density curve for a population.a. What proportion of the population is between 2 and 4?b. If a value is chosen at random from this population, what is the probability that
Provide an example of a Poisson random variable and explain how each condition for the Poisson distribution is fulfilled.
Twenty percent of the men in a certain community are more than 6 feet tall. An anthropologist samples five men from a large family in the community and counts the number X who are more than 6 feet
Provide an example of a binomial random variable and explain how each condition for the binomial distribution is fulfilled.
When a population mean is unknown, people will often approximate it with the mean of a large sample. Explain why this is justified.
If a business decision has an expected gain, is it possible to lose money? Explain.
Provide an example of a continuous random variable and explain why it is continuous.
Provide an example of a discrete random variable and explain why it is discrete.
Congenital disease: The connexin-26 mutation is a genetic mutation that results in deafness. The probability that a person carries a gene with this mutation is 0.0151. Use the Poisson approximation
Standard deviation: Refer to Exercise 12.Find the standard deviation of the number of particles that are withdrawn.
Mean: Refer to Exercise 12.Find the mean number of particles that are withdrawn.
Suspensions: The concentration of particles in a suspension is 2 per milliliter. A volume of 3 milliliters is withdrawn.Find the following probabilities.a. P(Exactly five particles are withdrawn)b.
Survey sample: In a college with 5000 students, 100 are randomly chosen to complete a survey in which they rate the quality of the cafeteria food. Let X be the number of freshmen who are chosen. Does
Rain, rain, go away: Let X be the number of days during the next month that it rains. Does X have a binomial distribution?Why or why not?
Reading tests: According to the National Center for Education Statistics, 66% of fourth graders could read at a basic level in 2007. Suppose that eight fourth graders are randomly selected.a. Find
Looking for a job: According to the General Social Survey conducted at the University of Chicago, 59% of employed adults believe that if they lost their job, it would be easy to find another one with
If the dice come up 11, your profit is $15. If the dice don’t come up 11, you lose $1. The probability that the dice come up 11 is 1∕18. What is the expected value of your profit? Is it an
Craps: In the game of craps, you may bet $1 that the next roll of the dice will be an
Genetic disease: Sickle-cell anemia is a disease that results when a person has two copies of a certain recessive gene.People with one copy of the gene are called carriers. Carriers do not have the
Lottery tickets: Several million lottery tickets are sold, and 60% of the tickets are held by women. Five winning tickets will be drawn at random.a. What is the probability that three or fewer of the
AP tests again: During a recent academic year, approximately 1.7 million students took one or more AP tests. Following is the frequency distribution of the number of AP tests taken by students who
AP tests: Advanced Placement (AP) tests are graded on a scale of 1 (low) through 5 (high). The College Board reported that the distribution of scores on the AP Statistics Exam in 2009 was as
Mean, variance, and standard deviation: A random variable X has the following probability distribution.a. Find the mean of X.b. Find the variance of X.c. Find the standard deviation of X. x 6 7 89 10
Which are distributions? Which of the following tables represent probability distributions? a. x P(x) b. x P(x) C. x P(x) d. x P(x) 3 0.35 5 0.27 0 0.02 2 0.10 4 0.20 6 0.45 1 0.34 3. 0.07 5 0.18 7
Huntington’s disease is a genetically transmitted disease that causes degeneration of nerve cells in the brain. The probability that a person carries a gene for Huntington’s disease is 0.00005
What are the variance and standard deviation of the number of messages received in an 8-hour period?
Refer to Problem
The number of text messages received on a certain person’s cell phone follows a Poisson distribution with the rate of 10 messages per hour. What is the mean number of messages received in an 8-hour
The number of large packages delivered by a courier service follows a Poisson distribution with a rate of 5 per day. Find the probability thata. Exactly 4 large packages are delivered on a given
A meteorologist states that the probability of rain tomorrow is 0.4 and the probability of rain on the next day is 0.6.Assuming these probabilities are accurate, and that the rain events are
Find the mean and standard deviation for the number of defective batteries in the sample of size 50.
Refer to Problem
At a cell phone battery plant, 5% of cell phone batteries produced are defective. A quality control engineer randomly collects a sample of 50 batteries from a large shipment from this plant and
Find the standard deviation of the number of pets.
Refer to Problem
Find the mean number of pets.
Refer to Problem
Find the probability that a randomly selected family has:a. 1 or 2 petsb. More than 2 petsc. No more than 3 petsd. At least 1 pet
Refer to Problem
The following table presents a probability distribution for the number of pets each family has in a certain neighborhood.Construct a probability histogram. Number of pets Probability 01 2 3 4 0.4 0.2
Find the missing value that makes the following a valid probability distribution. x 2 3 5 8 10 P(x) 0.23 0.12 0.09 ? 0.37
Refer to Problem 2.a. Find the variance of the random variable X.b. Find the standard deviation of the random variable X.
Find the mean of the random variable X with the following probability distribution. -2 1 4 5 P(x) 0.3 0.2 0.1 0.4
Explain why the following is not a probability distribution. x 6 7 89 10 P(x) 0.32 0.11 0.19 0.28 0.03
Describe circumstances under which you would use a combination.
Describe circumstances under which you would use a permutation.
In practice, one must decide whether to treat two events as independent based on an understanding of the process that creates them. For example, in a manufacturing process that produces electronic
Sometimes events are in the form ‘‘at least’’ a given number. For example, if a coin is tossed five times, an event could be getting at least two heads. What would be the complement of the
Explain why the General Addition Rule P (A or B) = P (A) + P (B) − P (A and B) may be used even when A and B are mutually exclusive events.
If the odds of an event occurring are 5:8, what is the probability that the event will occur?
Since there are two winning outcomes out of six equally likely outcomes, the odds of winning are 2:4.Suppose that a pair of dice is rolled and the player wins if it comes up ‘‘doubles,’’ that
When it comes to betting, the chance of winning or losing may be expressed as odds. If there are n equally likely outcomes and m of them result in a win, then the odds of winning are m:(n − m),
Explain how you could use the law of large numbers to show that a coin is unfair by tossing it many times.
Bart chooses three books at random.a. What is the probability that the books on his shelf are statistics textbook, dictionary, and comic book, in that order?b. What is the probability that the
Bookshelf: Refer to Exercise
Bookshelf: Bart has six books: a novel, a biography, a dictionary, a self-help book, a statistics textbook, and a comic book.a. Bart’s bookshelf has room for only three of the books. In how many
Assume the student chooses three courses at random. What is the probability that she chooses English, mathematics, and biology?
Required courses: Refer to Exercise
Required courses: A college student must take courses in English, history, mathematics, biology, and physical education.She decides to choose three of these courses to take in her freshman year. In
Rainy weekend: Sally is planning to go away for the weekend this coming Saturday and Sunday. At the place she will be going, the probability of rain on any given day is 0.10. Sally says that the
Heart attack: The following table presents the number of hospitalizations for myocardial infarction (heart attack) for men and women in various age groups.a. What is the probability that a randomly
Female business majors: At a certain university, the probability that a randomly chosen student is female is 0.55, the probability that the student is a business major is 0.20, and the probability
Music to my ears: Jeri is listening to the songs on a new CD in random order. She will listen to two different songs, and will buy the CD if she likes both of them. Assume there are 10 songs on the
Defective parts: A process manufactures microcircuits that are used in computers. Twelve percent of the circuits are defective. Assume that three circuits are installed in a computer. Denote a
Stop that car: A drag racer has two parachutes, a main and a backup, that are designed to bring the vehicle to a stop at the end of a run. Suppose that the main chute deploys with probability 0.99,
Start a business: Suppose that start-up companies in the area of biotechnology have probability 0.2 of becoming profitable, and that those in the area of information technology have probability 0.15
Blood types: Human blood may contain either or both of two antigens, A and B. Blood that contains only the A antigen is called type A, blood that contains only the B antigen is called type B, blood
Statistics, anyone? Let S be the event that a randomly selected college student has taken a statistics course, and let C be the event that the same student has taken a chemistry course. Suppose P (S)
How are your grades? There were 30 students in last semester’s statistics class. Of these, 6 received a grade of A, and 12 received a grade of B. What is the probability that a randomly chosen
Colored dice: A six-sided die has one face painted red, two faces painted white, and three faces painted blue. Each face is equally likely to turn up when the die is rolled.a. Construct a sample
In a standard game of pool, there are 15 balls labeled 1 through 15.a. In how many ways can the 15 balls be ordered?b. In how many ways can 3 of the 15 balls be chosen and ordered?
A caterer offers 24 different types of dessert. In how many ways can 5 of them be chosen for a banquet if the order doesn’t matter?
The Roman alphabet (the one used to write English) consists of five vowels (a,e, i, o, u), along with 21 consonants (we are considering y to be a consonant). Gregory needs to make up a computer
Suppose that the slot machine is played 5 times in a row. What is the probability of winning at least once?
Refer to Problem
Individual plays on a slot machine are independent. The probability of winning on any play is 0.38. What is the probability of winning 3 plays in a row?
A student is chosen at random. Which of the following pairs of events are independent?i. A: The student was born on a Monday. B: The student’s mother was born on a Monday.ii. A: The student is
A jar contains 4 red marbles, 3 blue marbles, and 5 green marbles. Two marbles are drawn from the jar one at a time without replacement. What is the probability that the second marble is red, given
The owner of a bookstore has determined that 80% of people who enter the store will buy a book. Of those who buy a book, 60% will pay with a credit card. Find the probability that a randomly selected
A certain neighborhood has 100 households. Forty-eight households have a dog as a pet. Of these, 32 also have a cat.Given that a household has a dog, what is the probability that it also has a cat?

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