Kathy and her brother Clay recently ran in a local marathon. The distribution of finishing timefor women was approximately normal with mean 259 minutes and standard deviation 32minutes. The distribution of finishing time for men was approximately normal with mean 242minutes and standard deviation 29 minutes. (a) The finishing time for Clay was 289 minutes. Calculate and interpret the standardized scorefor Clay’s marathon time. Show your work. (b) The finishing time for Kathy was 272 minutes. What proportion of women who ran themarathon had a finishing time less than Kathy’s? Show your work. (c) The standard deviation of finishing time is greater for women than for men. What does thisindicate about the finishing times of the women who ran the marathon compared to thefinishing times of the men who ran the marathon?
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.
Kathy and her brother Clay recently ran in a local marathon. The distribution of finishing timefor women was approximately normal with mean 259 minutes and standard deviation 32minutes. The distribution of finishing time for men was approximately normal with mean 242minutes and standard deviation 29 minutes.
(a) The finishing time for Clay was 289 minutes. Calculate and interpret the standardized scorefor Clay’s marathon time. Show your work.
(b) The finishing time for Kathy was 272 minutes. What proportion of women who ran themarathon had a finishing time less than Kathy’s? Show your work.
(c) The standard deviation of finishing time is greater for women than for men. What does thisindicate about the finishing times of the women who ran the marathon compared to thefinishing times of the men who ran the marathon?
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