The physical performance of 24 female collegiate rowers with IDNA was campared w

ID: 3172650 • Letter: T

Question

The physical performance of 24 female collegiate rowers with IDNA was campared with 24 female collegiate rowers with normal iron status. Assume that training-session duration of female rowers with IDNA is Normally distributed with mean 58 minutes and standard deviation 11 minutes. Training-session duration of female rowers with normal iron status is Normally distributed with mean 69 minutes and SD 18 minutes.

c) WHat is the probability that the mean duration of the 24 rowers with IDNA is greater than the mean duration of the 24 rowers with normal iron status?

Explanation / Answer

Given,

IDNA

Normal

Sample size(n1)=24

Sample size(n2)=24

Mean(X1)=58

Mean(X2)=69

SD1=11

SD2=18

to find, probability that mean duration of IDNA is greater than mean duration of normal

we need to calculate the Z value

Z= (x1 - x2) - (µ1- µ2)/Sqrt(SD1^2/n1+SD^2/n2)

Z=58-69/sqrt(121/24+324/24)

Solving we get

Z= -2.55

the corresponding probability for Z= -2.55 is 0.4946

Hence the probability that mean duration of IDNA is greater than mean duration of normal is

(1-0.5-0.4946=0.0054 or 0.54%)