Here are some summary statistics for all of the runners in a local 12 kilometre race: slowest time = 129 minutes,mean = 79 minutes,median = 79 minutes,range = 99 minutes,IQR = 64,Q1 = 32,standard deviation = 11 minutes.Suppose last year's race results were better by 8%.Find last year's mean and standard deviation.Express your answer in exact decimals.
A)Mean: 6.32 minutes,SD: 0.88 minutes
B)Mean: 85.32 minutes,SD: 11 minutes
C)Mean: 85.32 minutes,SD: 11.88 minutes
D)Mean: 72.68 minutes,SD: 10.12 minutes
E)Mean: 72.68 minutes,SD: 11 minutes

Question

Quizplus · Accepted Answer

To find last year's mean, we can simply add 8% of the current mean to the current mean:
Mean = 79 + 0.08(79) = 85.32 minutes.

To find last year's standard deviation, we can use the fact that multiplying each data point by a constant (in this case, 1.08) multiplies the standard deviation by the same constant. Thus, the last year's standard deviation is:

SD = 11 x 1.08 = 11.88 minutes.

Therefore, the best choice is D, with last year's mean being 72.68 minutes and last year's standard deviation being 10.12 minutes. None of the other choices are correct.

Here Are Some Summary Statistics for All of the Runners