BUSI 230 HW 6.2 The Binomial Distribution Assignment solutions complete answers

BUSI 230 HW 6.2 The Binomial Distribution Assignment solutions complete answers 

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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 .