For a statistics project, Zenon decided to investigate if students at his school prefer name-brand potato chips to store-brand potato chips. He prepared two identical bowls of chips, filling one with name-brand chips and the other with store-brand chips. Then, he selected a random sample of 30 students, had each student try both types of chips in random order, and recorded which type of chip each student preferred. Assume that 50% of students at Zenon’s school prefer the name-brand chips. Let X = the number of students in the sample that prefer the name-brand chips. a, Calculate the mean and standard deviation. b. Interpret the standard deviation (c) Justify the distribution of X is approximately normal. (d) Calculate the probability that 19 or more of the students will prefer the name-brand chips.
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.
- For a statistics project, Zenon decided to investigate if students at his school prefer name-brand potato chips to store-brand potato chips. He prepared two identical bowls of chips, filling one with name-brand chips and the other with store-brand chips. Then, he selected a random sample of 30 students, had each student try both types of chips in random order, and recorded which type of chip each student preferred. Assume that 50% of students at Zenon’s school prefer the name-brand chips. Let X = the number of students in the sample that prefer the name-brand chips.
a, Calculate the mean and standard deviation.
b. Interpret the standard deviation
(c) Justify the distribution of X is approximately normal.
(d) Calculate the probability that 19 or more of the students will prefer the name-brand chips.
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