Binomial Probability

A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?
(Be able to use a table for this problem.)

P(X≥6)=P(6)+P(7)+P(8)+P(9)+P(10)=0.377

A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 26 components and accept the whole batch if there are fewer than 3 defectives. If a particular shipment of thousands of components actually has a 5% rate of defects, what is the probability that this whole shipment will be accepted?
(calculator/ key sequence)

P(X<3)=binomcdf(26,.05,2)=0.861

A car insurance company has determined that 8% of all drivers were involved in a car accident last year. Among the 14 drivers living on one particular street, 3 were involved in a car accident last year. If 14 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year?
(calculator/ key sequence)

P(X≥3)=1 - binomcdf(14, .08, 2)= .0958

In a certain college, 33% of the physics majors belong to ethnic minorities. If 15 students are selected at random from the physics majors, that is the probability that no more than 10 belong to an ethnic minority?
(calculator/ key sequence)

P(X≤10)=binomcdf(15, .33, 10)=.998

An airline estimates that 98% of people booked on their flights actually show up. If the airline books 71 people on a flight for which the maximum number is 69, what is the probability that the number of people who show up will exceed the capacity of the plane?
(Be able to do this by hand/formula.)

P(X>69)= P(70) + P(71)= .5835

In a study, 38% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 10 adults randomly selected from this area, only 1 reported that their health was excellent. Find the probability that when 12 adults are randomly selected, fewer than 2 are in excellent health.
(Be able to do this by hand/formula.)

P(x<3)= P(0) + P(1) =.0598

A test consists of 10 multiple choice (A,B,C,D,E) questions. To pass the test a student must answer more than half of the questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?
(Be able to use a table for this problem.)

P(X>5)=P(6)+P(7)+P(8)+P(9)+P(10)=.006

Find the probability of no girls in 4 births. Assume that male and female births are equally likely and that the births are independent events.
(calculator/ key sequence)

P(0)=binompdf(4, 0.5, 0)=.0625

Find the probability of a perfect score on a quiz with 5 true/false, if every answer is a random guess.
(calculator/ key sequence)

P(5)= binompdf (5, 0.5, 5)=.03125

Binomial Probability

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