For an intramural sports program at a particular college, the time to run one mile is recorded for 200 male students in the program. These times are approximately normal with mean 8 minutes and standard deviation 1 minute. For the same intramural sports program at the same college, the time to run one mile is recorded for 50 female students in the program. These times are approximately normal with mean 7.5 minutes and standard deviation 2 minutes. Devon participates in the intramural program for men. His best time to run the mile is 6.6 minutes. Kendall participates in the intramural program for women. Her best time to run the mile is 5.7 minutes. Who ran the mile faster relative to their gender?

Devon has the lower z-score, so he ran the mile faster relative to his gender.

Step-by-step explanation:

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Who ran the mile faster relative to their gender?

The lower the percentile of time ran, the faster. So whoever has the lower z-score ran the mile faster.

Devon

His best time to run the mile is 6.6 minutes.

These times are approximately normal with mean 8 minutes and standard deviation 1 minute.

We have to find Z when . So

Kendall

Her best time to run the mile is 5.7 minutes.

These times are approximately normal with mean 7.5 minutes and standard deviation 2 minutes.

We have to find Z when . So

Devon has the lower z-score, so he ran the mile faster relative to his gender.

throw the computer

step-by-step explanation:

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:

here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so and .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.