Binomial Mean and Variance

An algebra 2 test has 6 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 6 questions, what is the probability that you get exactly 3 questions correct?

• 0.962

• 0.132

• 0.831

• 0.250

Which of the following is NOT an assumption of the Binomial distribution?

• All trials must be independent.

• Each trial must be classified as a success or a failure.

• All trials are dependent on each other.

• The number of successes in the trials is counted.

Find the standard deviation of a binomial distribution with n=50 and p=0.4 (Round to the nearest tenth)

• 4.2

• 3.5

• 12.0

• 6.2

In a survey of 1000 people, what is the formula for calculating the variance of the number of people who prefer tea over coffee, assuming a binomial distribution?

• n*p^2*(1-p)

• n^2*p*(1-p)

• n*p*(1-p)^2

• n*p*(1-p)

Find the mean, variance, and standard deviation for each of the values of n and p when the conditions for the binomial distribution are met.

n=100, p=0.75

Type your final answer as follows:

Mean =

Variance =

SD =

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Answer explanation

mean = 75

variance = 18.75

SD = 4.33

Assuming that a normal distribution is a reasonable approximation for a binomial distribution, what value is used to approximate the mean?

• nq

• np

• n/p

• n/q

Assuming that a normal distribution is a reasonable approximation for a binomial distribution, what value is used to approximate the standard deviation?

• npq

• np

• √np

• √npq

Given that a class consists of 30 students, 70% of them pass in a mathematics test. Find the variance and the standard deviation of the number of students pass the test. (Separate your answer with a ',' ie. 2.30 , 1.115)