Binomial Probabilities Practice

COC Math 140 Binomial Probabilities Practice

Many probabilities are binomial in nature. When we collect a random sample of size n from a population and the data collected falls into just two outcomes, we call this binomial. The two outcomes are often called success and failure. The probability of success is p and must be the same for every trial. Also each outcome must be independent of one another. The probability of X successes in n trials can be calculated using StatCrunch

Directions: For each of the following, verify that the situation is binomial in nature and find the number of trials n, the number of outcomes X, and the probability of success p. Then use StatCrunch to find the given probabilities.

1. Steve Nash is one of the best free throw shooters in the NBA. The probability he will make a free throw is 92%. Let us suppose that Nash shoots 16 free throws in a game.

What is the probability that he makes exactly 13 free throws out of the 16 tries? What is the probability that he makes less than 12 free throws in the game? What is the probability that he makes 14 or more free throws in the game?

2. Suppose that a company manufactures I-pads. It has been found that 3% of the I- pads made will be defective. The company ships a box of 50 total I-pads.

What is the probability that the box will contain exactly 4 defective I-pads? What is the probability that the box will contain 3 or less defective I-pads? What is the probability that the box contains 5 or more defective I-pads?

3. A car company found that their Minivan transmissions have a 12% defective rate. A total of 72 Minivans were brought in for service this month.

What is the probability that exactly 9 of them need to have their transmission replaced? What is the probability that more than 10 of the minivans will need their transmission replaced? What is the probability that 6 or less of the minivans will need their transmission replaced?

Courtesy of Matt Teachout