Question

What is the probability that the mean duration of the 24 rowers with idna exceeds 63 minutes?

Answer 1

Explanation:

Given that: Training-session duration of female rowers with normal iron status is Normally distributed, with mean 69 minutes and standard deviation 18minutes.

Solution:

z score shows the relationship between sample means. The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by the formula:

`z=(x-\mu)/(\sigma)\\\\for\ sample(n):\\\\z=(x-\mu)/(\sigma/√(n) ) \\\\where\ \mu=mean,\sigma=standard\ deviation,x=raw\ score`

Given that μ = 69 minutes, σ = 18 minutes, n = 24

For x > 63 minutes:

`z=(x-\mu)/(\sigma / √(n) ) =(63-69)/(18/√(24) )=-1.63`

From the distribution table, P(x > 63) = P(z > -1.63) = 1 - P(z < 1.63) = 1 - 0.0516 = 0.9484