statistics
posted by lauren .
An important indicator of lung function is forced expiratory volume(FEV), which is the volume of air that a person can expire in one second. Dr. Jones plans to measure FEv in a random sample of n young women from a certain population, and to use the sample mean as an estimate of the population mean. Let E be the event that Jones's sample mean will be within + 100mLi of the population mean.Assume that the population distribution is normal with mean 3000 mLi and standard deviation 400 mLi. Find Pr{E} if:
A)n=15

mean of sample means = mean of population = 3000
sigma sample means = sigma population/sqrt n
so s sample mean = 400/sqrt(15)
= 103
100/103 = .971 s
so we are interested in between the mean .971 sigma to the mean +.971 sigma
from tables of normal distribution you can get the probability of being beyond mean +.971 sigma
it is 1.834 = .166
by symmetry the probability of being below mean .971 sigma is also .166
so the probability of being above or below the desired range i 2*.166 = .332
so the probability of being within the desired range is
1.332 = .668 or 67 %
This makes sense because we all know that about 68 % lies within 1 sigma and we are at almost 1 sigma, namely .971 sigma
Respond to this Question
Similar Questions

Statistics
A recent study was designed to compare smoking habits of young women with those of young men. A random sample of 150 women revealed that 45 smoked. A random sample of 100 men indicated that 25 smoked. At the 0.05 significance level … 
Physics
A submarine has run into trouble and is stuck at the bottom of the ocean. Several people are on board and must make their way to the surface without any diving gear. The air pressure aboard the submarine is 3.29 atm. air temperature … 
PHYSICS
A submarine has run into trouble and is stuck at the bottom of the ocean. Several people are on board and must make their way to the surface without any diving gear. The air pressure aboard the submarine is 3.04 atm. The air temperature … 
statistics
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose … 
Biology
In a lab on lung capacity where lung volumes (Tidal Volume, Expiratory Reserve Volume, Inspiratory Capacity, Inspiratory Reserve Volume, and Vital Capacity) are measured... Why can't you measure the Inspiratory Reserve Volume (IRV) … 
Biology
In a lab on lung capacity where lung volumes (Tidal Volume, Expiratory Reserve Volume, Inspiratory Capacity, Inspiratory Reserve Volume, and Vital Capacity) are measured... Why can't you measure the Inspiratory Reserve Volume (IRV) … 
statistics
A group of scientists is studying whether a new medical treatment has an adverse (bad) effect on lung function. Here are data on a simple random sample of 10 patients taken from a large population of patients in the study. Both variables … 
Statistics
Dr. Hernandez plans to measure FEV in a random sample of n young women from a certain popu lation, and to use the sample mean y ̄ as an estimate of the population mean. Let A be the event that Hernandezâ€™s sample mean will be … 
Gr 11 Biology
if you were a snoker, what lung volumes (tidal volume, expiratory reserve volume or vital capacity) would be most affected? 
stat
The heights of young American women, in inches, are normally distributed with mean mu and standard deviation 2.4 (sigma). I select a simple random sample of four young American women and measure their heights. The four heights, in …