1. This problem involves inspection at a widget factory. Assume that a box contains 2 defective widgets and 9 acceptable widgets. There are 3 inspectors, each of whom selects a widget from the box at random, inspects it, and then replaces it in the box. Each inspector makes his or her inspection at a different time. What is the probability that at least one inspector will find a defective widget?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
1. This problem involves inspection at a widget factory. Assume that a box contains 2 defective widgets and 9 acceptable widgets. There are 3 inspectors, each of whom selects a widget from the box at random, inspects it, and then replaces it in the box. Each inspector makes his or her inspection at a different time.
What is the probability that at least one inspector will find a defective widget?
2. Rework problem 23 from section 4.1 of your text involving a basketball player's three point shooting. Assume that his shots are Bernoulli trials, and that he makes 1 in 5 of his shots.
How many three point shots must the player attempt so that the probability of his hitting at least one of them is at least 0.98?
3. Rework problem 25 from section 4.1 of your text involving a car saleswoman. Assume that showing a car is a Bernoulli trial, and each time she shows a car, there is a probability of 0.05 that the customer will buy the car. The saleswoman has a goal of selling at least one car a week.
How many cars must she show so that the probability of her reaching her goal is at least 0.53?
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