Binomial Distribution

Is the distribution below a probability distribution? Why or why not?

• Yes. All P(x) values are between 0 and 1, and ∑P(x) = 1

• No, not all P(x) values are between 0 and 1.

• No, ∑P(x) ≠ 1.

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

The student who makes the morning announcements has the bad habit of saying “like” all the time. The chance that they say “like” in a sentence is 60%. You decide to keep a tally of how many times they say like. If they say 350 sentences this week, what is the probability that they will say “like” at least 200 times?

• 0.87

• 0.13

• 0.85

• 0.15

True or False:

exactly = binompdf

at most = binomcdf

at least = binomcdf

• True

• False

The parameters of the binomial distribution are n (​ (a)   ) and p (​ (b)   ) on any one trial.

• the number of trials

• the probability of a 'success'

X is a binomial distribution with mean 8 and variance 6.4.

Then, the value of np = ​ (a)   , npq = ​ (b)   , q = ​ (c)   , p = ​ (d)   , and n = ​ (e)   .

• 8

• 6.4

• 0.8

• 0.2

• 40

X is a binomial distribution with mean 8 and variance 6.4.

Find (X ≤ 1).

(Write down your answer into 3 s.f.)

Jakob is a dentist who finds that, on average, one in five of his patients does not turn up for their appointment. Using a binomial distribution, find the mean of the number of patients who turn up for their appointments, in a clinic with 20 appointments.

Jakob is a dentist who finds that, on average, one in five of his patients does not turn up for their appointment. Using a binomial distribution, find the variance of the number of patients who turn up for their appointments, in a clinic with 20 appointments.

Which of the following is false about binomial probabilities?

• Their distributions are approximately symmetric.

• Trials must be fixed.

• Events musts be independent.

• The probability of success must be 0.50