We saw two distributions for triathlon times: N (μ = 4313, σ = 583) for Men, Ages 30 - 34 and N (μ = 5261, σ = 807) for the Women, Ages 25 - 29 group. Times are listed in seconds. Use this information to compute each of the following:

a. The cutoff time for the fastest 5% of athletes in the men's group, i. e. those who took the shortest 5% of time to finish.
b. The cutoff time for the slowest 10% of athletes in the women's group.

Step-by-step explanation:

Hello!

Using the information of the triathlon times of men and women you have to find:

a. The cutoff time for the fastest 5% men, if the times of the male triathletes have a normal distribution, this value will separate the top 5% from the rest of the distribution, symbolically:

P(X≥x₀)= 0.05

Where x₀ represents the cutoff time that you need to find.

Now if this value has 5% of the distribution above it, then 95% of the distribution will be below it, symbolically:

P(X<x₀)= 0.95

Next is to use the standard normal distribution, you have to find the Z value that accumulates 0.95 of probability: P(Z<z₀)= 0.95

z₀= 1.648

Using the formula: Z= (X-μ)/δ what is left to do is to reverse the standardization and reach the value of the variable:

z₀= (x₀-μ)/δ

x₀= (z₀*δ)+μ

x₀= (1.648*583)+4313

x₀= 5273.784 seconds

The cutoff time for the fastest 5% is 5273.784 seconds.

b. The cutoff time for the slowest 10% women, if you are taking the "slowest" into account, then this is the lowes 10% of the distribution. Meaning that the value of time separates the "lowest" 10% of the distribution from the rest, symbolically:

P(X≤x₀)=0.10

Same as before, you have to use the standard normal distribution:

P(Z≤z₀)= 0.10

z₀= - 1.283

Now using this value you have to reverse the standardization:

z₀= (x₀-μ)/δ

x₀= (z₀*δ)+μ

x₀= (-1.283*807)+5261

x₀= 4225.619 seconds

The cutoff time for the slowest 10% is 4225.619 seconds.

I hope it helps!

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕

is there a question here?

step-by-step explanation: