BUSI 230 HW 6.1, HW 6.2, HW 7.1, HW 7.2 Connect Exercises Week 4 solutions complete answers

BUSI 230 HW 6.1, HW 6.2, HW 7.1, HW 7.2 Connect Exercises Week 4 solutions complete answers 

 

BUSI 230 HW 6.1 Random Variables Assignment 

 

Select the appropriate word or phrase to complete the sentence.

A numerical outcome of a probability experiment is called .

The sum of all the probabilities in a discrete probability distribution must be equal to .

 

Determine whether the random variable described is discrete or continuous.

The length of life of a washing machine.

The weight of a randomly chosen student's backpack.

The temperature readings by a randomly selected city in the month of August.

The number of spades in a 5 card poker hand dealt from an ordinary deck of 52 cards.

The number of dental visits a randomly chosen person had for the past 5 years.

The time of a randomly chosen city employee to get to work.

The number of pets a randomly chosen family may have.

The time it takes to drive to the airport.

The number of people in line at the bank at a randomly chosen time.

The number of attendees at a cinema on a Friday night.

The amount of time of a randomly chosen college student to complete a statistical final exam.

 

Find the similar data and choose the answer

Determine whether the table represents a discrete probability distribution. Explain why or why not.

 

Compute the mean and standard deviation of the random variable with the given discrete probability distribution.

(a) Find the mean. Round the answer to three decimal places, if necessary.

(b) Find the standard deviation. Round the answer to at least three decimal places.

 

Fill in the missing value so that the following table represents a probability distribution.

 

Put some air in your tires: Let X represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of X is as follows.

 

Texting: Five teenagers are selected at random. Let X be the number of them who have sent text messages on their cell phones within the past 30 days. According to a study by the Nielsen Company, the probability distribution of X is as follows:

 

Lottery: In the New York State Numbers lottery, you pay $3 and can bet that the sum of the numbers that come up is 13. The probability of winning is 0.095, and if you win, you win $8.50, which is a profit of $5.5. If you lose, you lose $3.

(a) What is the expected value of your profit? Round the answer to two decimal places.

(b) Is it an expected gain or an expected loss? Round the answer to two decimal places.

 

Craps: In the game of craps, a pair of dice are rolled, and people bet on the outcome. For example, you can bet $1 that the dice will total 2. The probability that you win is 1/36, and if you win, your profit is $30. If you lose, you lose $1.

(a) What is the expected value of your profit? Round the answer to two decimal places.

(b) Is it an expected gain or an expected loss? Round the answer to two decimal places.

 

Liberty University BUSI 230 HW 6.2 The Binomial Distribution Assignment complete solutions answers and more!

 

How many possible outcomes are there for each trial in a binomial distribution?

In a binomial distribution, there are  possible outcomes for each trial.

 

Determine whether the random variable  has a binomial distribution. If it does, state the number of trials . If it does not, explain why not.

Ten students are randomly chosen from a Statistics class of 300 students. Let  be the number of students that earned an A in the class.

Six students are randomly chosen from a Statistics class of 300 students. Let  be the average student grade on the first test.

Ten students are randomly chosen from a statistics class of 300 students. Let X be the average grade of these students.

A fair coin is flipped 5 times. Let X be the number of times the coin lands Tails.

A fair die is rolled 2 times. Let X be the sum of the two numbers observed.

A fair die is rolled 30 times. Let X bet the number of times an odd number appears.

A coin is flipped until a Head appears. Let X be the number of Heads.

Thirty students are randomly chosen from a small college with an enrollment of 2400. Let X be the number who are freshmen students.

Ten cards are randomly drawn with replacement from a standard deck of 52. Let X be the number of Hearts drawn.

Twenty students are randomly chosen from a math class of 70 students. Let X be the total number of student absences.

Choose the statement that explains why X does not have a binomial distribution. More than one may apply.

 

Determine the probability  for a binomial experiment with n=11 trials and success probability p=0.3. Then find the mean, variance, and standard deviation.

Determine the probability P(6). Round the answer to at least four decimal places.

Find the variance and standard deviation. Round the variance to at least two decimal places and standard deviation to at least three decimal places.

 

Determine the probability P(More than 13). Round the answer to at least four decimal places.

 

Take a guess: A student takes a multiple-choice test that has 8 questions. Each question has two choices. The student guesses randomly at each answer. Let  be the number of questions answered correctly.

 

Your flight has been delayed: At Denver International Airport, 82% of recent flights have arrived on time. A sample of 11 flights is studied.

(a) Find the probability that all 11 of the flights were on time.

(b) Find the probability that exactly 9 of the flights were on time.

(c) Find the probability that 9 or more of the flights were on time.

(d) Would it be unusual for 10 or more of the flights to be on time? Use a cutoff of 0.05.

 

Blood types: The blood type O negative is called the "universal donor" type, because it is the only blood type that may safely be transfused into any person. Therefore, when someone needs a transfusion in an emergency and their blood type cannot be determined, they are given type O negative blood. For this reason, donors with this blood type are crucial to blood banks. Unfortunately, this blood type is fairly rare; according to the Red Cross, only 7% of U.S. residents have type O negative blood. Assume that a blood bank has recruited 25 donors.

(a) What is the mean number of donors who have type O negative blood? Round the answer to two decimal places.

(b) What is the standard deviation of the number of donors who have type O negative blood? Round the answer to four decimal places.

 

Coronary bypass surgery: A healthcare agency reported that 51% of people who had coronary bypass surgery in 2008 were over the age of 65. Seventeen coronary bypass patients are sampled.

(a)What is the probability that exactly 11 of them are over the age of ? Round the answer to four decimal places.

(b)What is the probability that more than 12 are over the age of ? Round the answer to four decimal places.

(c)What is the probability that fewer than 9 are over the age of ? Round the answer to four decimal places.

(d)Would it be unusual if all of them were over the age of ? Use a cutoff of .

 

Liberty University BUSI 230 HW 7.1 The Standard Normal Curve Assignment complete solutions answers and more!

 

Select the appropriate word or phrase to complete the sentence.

If  is a continuous random variable, then   for any number .

A normal distribution with mean  and standard deviation  is called the  normal distribution.

The mean, median, and mode of a normal distribution are  each other.

A normal distribution with mean  and standard deviation  is called the  normal distribution.

For a standard normal distribution, points on the horizontal axis to the right of the mode have  -scores.

For a standard normal distribution, points on the horizontal axis to the left of the mode have  -scores.

 

The following figure is a normal curve that represents the approximate heights, in inches, of adult women in the United States.

(a) Find the proportion of cats who weigh more than  pounds.

(b) Find the proportion of cats who weigh less than  pounds.

(c) Find the proportion of cats who weigh between  and  pounds.

 

Find each of the shaded areas under the standard normal curve using a TI-84 calculator. Round the answers to four decimal places.

The area of the shaded region is

 

Find the area under the standard normal curve to the left of the following -values. Round the answers to four decimal places.

(a)Find the area under the standard normal curve to the left of z=2.21.

(b)Find the area under the standard normal curve to the left of z=-1.30.

 

Find the area under the standard normal curve to the right of the following -values. Round the answers to four decimal places.

(a)Find the area under the standard normal curve to the right of z=0.78.

(b)Find the area under the standard normal curve to the right of z=-1.81.

 

Find the area under the standard normal curve that lies between the following -values. Round the answers to four decimal places.

(a) Find the area under the standard normal curve that lies between z=0.47 and z=1.53.

(b) Find the area under the standard normal curve that lies between z=-0.29 and z=-2.26.

 

Find the area under the standard normal curve that lies outside the interval between the following -values. Round the answers to four decimal places.

(a)Find the area under the standard normal curve that lies outside of the interval between z=1.36 and z=1.78.

(b)Find the area under the standard normal curve that lies outside of the interval between z=-0.42 and z=2.47.

 

Use Excel to find the -score for which the area to its left is 0.61. Round the answer to two decimal places.

The z-score for the given area is

 

Use Excel to find the -score for which the area to its right is 0.42. Round the answer to two decimal places.

The z-score for the given area is

 

Use Excel to find the z-scores that bound the middle 90% of the area under the standard normal curve. Enter the answers in ascending order. Round the answers to two decimal places.

The -scores for the given area are

 

Liberty University BUSI 230 HW 7.2 Applications of the Normal Distribution Assignment complete solutions answers and more!

 

A value that is one standard deviation above the mean will be a -score of .

A value that is one standard deviation below the mean will be a -score of .

A value that is two standard deviations above the mean will be a -score of .

A value that is two standard deviations below the mean will be a -score of .

A value that is three standard deviations above the mean will be a -score of .

A value that is three standard deviations below the mean will be a -score of .

 

A normal population has mean u=9 and standard deviation =5.

(a) What proportion of the population is less than 19?

(b) What is the probability that a randomly chosen value will be greater than 4?

 

A normal population has mean u=37 and standard deviation =9.

(a) What proportion of the population is between 18 and 28?

(b) What is the probability that a randomly chosen value will be between 31 and 41?

 

A normal population has mean u = 57 and standard deviation = 8. What is the 87th percentile of the population? Use the TI-84 Plus calculator. Round the answer to at least one decimal place.

 

Baby weights: The weight of male babies less than 2 months old in the United States is normally distributed with mean 11.7 pounds and standard deviation 2.9 pounds. Use Excel to answer the following. Round the answers to four decimal places.

(a) What proportion of babies weigh more than 14 pounds?

(b) What porportion of babies weigh less than 15 pounds?

(c) What proportion of babies weigh between 11.2 and 16 pounds?

(d) Is it unusual for a baby to weigh more than 17 pounds?

 

Check your blood pressure: In a recent study, the Centers for Disease Control and Prevention reported that diastolic blood pressures (in ) of adult women in the United States are approximately normally distributed with mean 80.6 and standard deviation 9.7.

(a) Find the 30th percentile of the blood pressures.

(b) Find the 33rd percentile of the blood pressures.

(c) Find the third quartile of the blood pressures.

 

Baby weights: The weight of male babies less than 2 months old in the United States is normally distributed with mean 12 pounds and standard deviation 3.7 pounds.

(a) Find the 84th percentile of the baby weights.

(b) Find the 13th percentile of the baby weights.

The third quartile of the baby weights is  pounds.

 

Tire lifetimes: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean =41  and standard deviation  =6. Use the TI-84 Plus calculator to answer the following.

(a) What is the probability that a randomly chosen tire has a lifetime greater than 47 thousand miles?

(b) What proportion of tires have lifetimes between 36 and 45 thousand miles?

(c) What proportion of tires have lifetimes less than 44 thousand miles?

 

Tire lifetimes: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean  =41  and standard deviation  =5. Use the TI-84 Plus calculator to answer the following.

(a) Find the 16th percentile of tire lifetimes.

(b) Find the 68th percentile of tire lifetimes.

(c) Find the third quartile of the tire lifetimes.

(d) The tire company wants to guarantee that its tires will last at least a certain number of miles. What number of miles (in thousands) should the company guarantee so that only 3% of the tires violate the guarantee?