in a 2003 study, the Accreditation Council for Graduate Medical Education found that medical residents' mean number of hors worked in a week in 81.7. suppose the number of hours worked per week by medical residents is approximately normally distributed with a standard deviation of 6.9 hours.
1) determine the 75th percentile for the number of hours worked in a week by medical residents.
2) determine the number of hours worked in a week that makes up the middle 80% of medical residents. justify and explain your reasoning

Question

in a 2003 study, the Accreditation Council for Graduate Medical Education found that medical residents' mean number of hors worked in a week in 81.7. suppose the number of hours worked per week by medical residents is approximately normally distributed with a standard deviation of 6.9 hours. 
1) determine the 75th percentile for the number of hours worked in a week by medical residents.
2) determine the number of hours worked in a week that makes up the middle 80% of medical residents. justify and explain your reasoning

anonymous · Answer

You need to convert the figure of 75 hours to a z-value (because this is the parameter used in the normal distribution tables), using the formula

z = (x - μ )/s.d

So z = - 6.7 / s.d.

But when you are considering the mean of a sample (as opposed to the value for a single individual), the standard deviation diminishes as the size of the sample increases, according to the function

s.d = σ / √n (where σ is the population standard deviation)

So for the first sample, s.d. = 6.9/√5 = 3.0858, and z = - 6.7/3.0858 = - 2.171

And from the table of areas of the normal distribution, P(x < - 2.171) = 0.0148


Second sample similarly, s.d = 6.9/√8 = 2.4395,

hence z = - 2.7464, and P(x< - 2.7464) = 0.00301

anonymous · Answer

Its Right ! (:

anonymous · Answer

thank you so much for your help guys :) @Yumira

anonymous · Answer

Welcome :D