A small city has three automobile dealerships: a GM dealer selling Chevrolets and Buicks; a Ford dealer selling Fords and Lincol
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Answer:
a) Clay's marathon time is 1.62 standard deviations above the mean finishing time for men.
b) 69.51% of those who ran the marathon has a finishing time less than 272.
c) The spread in the distribution of women's finishing time is greater as compared to the spread in the distribution of men's finishing time.
Step-by-step explanation:
Part a) It was given that, the finishing time for Clay's marathon time is 289 minutes.
To calculate the standardized test score for Clay's marathon time, we use the formula:
where
and
We substitute the values into the formula to get:
Interpretation: Clay's marathon time is 1.62 standard deviations above the mean finishing time for men.
b) To calculate the proportion of women that had a finishing time less than Kathy , we again need to calculate the z-score for x=272, with mean for women being 259 minutes and standard deviation 32 minutes.
We substitute to get:
From the standard normal distribution table, P(z<0.41)=0.6951
Therefore 69.51% of those who ran the marathon has a finishing time less than 272.
c) The standard deviation measures the variation of a distribution. This means the standard deviation measures how far away the data set of a distribution are from the mean.
If the standard deviation of finishing time is greater for women than for men, then it indicates that, women's finishing time are far away from the mean finishing time as compared to men's finishing time.