Suppose a company manufactures wooden chairs. The manufacturing process has two main components, sanding and varnishing. Suppose on average, each chair takes 18 minutes to sand, with a standard deviation of 4 minutes. After sanding, employees have a fixed 2 minute interval for the dust to settle from the chairs. Then, employees varnish the chairs. Varnishing on average takes 21 minutes with a standard deviation of 5 minutes. Assume sanding and varnishing times are independent of each other, and the entire process has a distribution that is approximately normal. a. Describe the distribution of the combined total process of sanding and varnishing. b. Find the probability that a randomly selected chair takes more than 45 minutes for the entire sanding and varnishing process. c. Suppose 6 chairs are randomly selected. What is the probability all of these chairs take more than 45 minute for the entire sanding and varnishing process? d. Suppose 6 chairs are randomly selected. What is the probability at least one of these chairs take more than 4 minutes for the entire sanding and varnishing process?

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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.