COC Math 140
Binomial Probabilities PracticeANSWERS
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?
The probability that Nash will make exactly 13 free throws out of the 16 tries is about 0.097.
What is the probability that he makes less than 12 free throws in the game?
The probability that he makes less than 12 free throws in the game is about 0.007.
What is the probability that he makes 14 or more free throws in the game?
The probability that he makes 14 or more free throws in the game is about 0.869.
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?
The probability that the box will contain exactly 4 defective i-pads is about 0.046.
What is the probability that the box will contain 3 or less defective i-pads?
The probability that the box will contain 3 or less defective i-pads is about 0.937.
What is the probability that the box contains 5 or more defective i-pads?
The probability that the box contains 5 or more defective i-pads is about 0.017.
- 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?
The probability that exactly 9 of the Minivans need to have their transmission replaced is about 0.140.
What is the probability that more than 10 of the Minivans will need their transmission replaced?
The probability that more than 10 of the Minivans will need their transmission replaced is about 0.242.
What is the probability that 6 or less of the Minivans will need their transmission replaced?
The probability that 6 or less of the Minivans will need their transmission replaced is about 0.224.
Courtesy of Matt Teachout