Question

Watch your cholesterol: The mean serum cholesterol level for U.S. adults was 197, with a standard deviation of 38 (the units are milligrams per deciliter). A simple random sample of 105 adults is chosen. Use the TI-84 calculator. Round the answers to four decimal places. Part 1 of 3 What is the probability that the sample mean cholesterol level is greater than 206? The probability that the sample mean cholesterol level is greater than 206 is Part 2 of 3 What is the probability that the sample mean cholesterol level is between 183 and 195? The probability that the sample mean cholesterol level is between 183 and 195 is Part 3 of 3 Would it be unusual for the sample mean to be less than 192? It (Choose one) V be unusual for the sample mean to be less than 192, since the probability is

Answer 1

1)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	197
std deviation   =σ=	38.000
sample size       =n=	105
std error=σx̅=σ/√n=	3.7084

probability =

P(X>206)

=

P(Z>2.43)=

1-P(Z<2.43)=

1-0.9924=

0.0076

2)

probability =

P(183<X<195)

=

P(-3.78<Z<-0.54)=

0.2948-0.0001=

0.2948

3)

probability =

P(X<192)

=

P(Z<-1.35)=

0.0888

it will not be unusual..........is 0.0888