Hanover High School has the best women's swimming team in the region. The 400-meter freestyle relay team is undefeated this year. In the 400-meter freestyle relay, each swimmer swims 100 meters. The times, in seconds, for the four swimmers this season are approximately normally distributed with means and standard deviations as shown.

Complete question :

Swim team Hanover High School has the best women’s swimming team in the region. The 400- meter freestyle relay team is undefeated this year. In the 400-meter freestyle relay, each swimmer swims 100 meters. The times, in seconds, for the four swimmers this season are approximately Normally distributed with means and standard deviations as shown. Assuming that the swimmer’s individual times are independent, find the probability that the total team time in the 400-meter freestyle relay is less than 220 seconds. Follow the four-step process

0.225

Step-by-step explanation:

Given the data:

Swimmer__ Mean __Std. dev.

Wendy ___ 55.2 2.8

Jill 58.0 3.0

Carmen56.3 2.6

Latrice54.72.7

Team average = (55.2 + 58 + 56.3 + 54.7) = 224.2

Team standard deviation = (2.8 + 3 + 2.6 + 2.7) = 11.1

Standard Error = 11.1 /sqrt(n)

Standard Error = 11.1 / sqrt(4)

Standard Error (S. E) = 11.1 / 2 = 5.55

P(x < 220) :

(x - mean) / S.E

(220 - 224.2) / 5.55

= −0.756756

P(Z < - 0.757) = 0.22452

P(Z < - 0.757) = 0.225

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer