Please explain in depth because I am very confused. a. The serum cholesterol lev
ID: 3040755 • Letter: P
Question
Please explain in depth because I am very confused.
a.
The serum cholesterol levels of a population of 12 to 14 year olds is normally distributed with a mean of 155 mg/dl, with a standard deviation of 27 mg/dl.
Suppose we take a sample of nine 12 to 14 year olds. What is the probability that the mean cholesterol level of the sample is between 140 and 150?
b.
Suppose we take a many different samples of nine 12 to 14 year olds and record their mean cholesterol.
What percent of these samples do you expect to have a mean cholesterol level between 140 and 150?
c.
Suppose we take a many different samples of nine 12 to 14 year olds and record their mean cholesterol.
You should expect about 95% of these samples will have a mean cholesterol level below what level?
Explanation / Answer
a)
b)
24.15 % of these samples we expect to have a mean cholesterol level between 140 and 150.
c)
for 95th percentile ; z score =1.645
hence corresponding level=mean +z*std deviation =155+1.645*9=169.80
for normal distribution z score =(X-)/ here mean= = 155.000 std deviation == 27 sample size =n= 9 std error=x=/n= 9.0000 probability = P(140<X<150) = P(-1.6667<Z<-0.5556)= 0.2893-0.0478= 0.2415