What are the steps to solve this problem? A simple random sample of size n = 49

Question

What are the steps to solve this problem?
A simple random sample of size n = 49 is obtained from a population with mean = 80 and standard deviation = 14. (8.1) a.) Describe the sampling distribution of X-bar.
b.) What is P(X-bar > 83)?
c.) What is P(X-bar < 75.8)?
d.) What is P(78.3 < X-bar < 85.1)?
What are the steps to solve this problem?
A simple random sample of size n = 49 is obtained from a population with mean = 80 and standard deviation = 14. (8.1) a.) Describe the sampling distribution of X-bar.
b.) What is P(X-bar > 83)?
c.) What is P(X-bar < 75.8)?
d.) What is P(78.3 < X-bar < 85.1)?
What are the steps to solve this problem?
A simple random sample of size n = 49 is obtained from a population with mean = 80 and standard deviation = 14. (8.1) a.) Describe the sampling distribution of X-bar.
b.) What is P(X-bar > 83)?
c.) What is P(X-bar < 75.8)?
d.) What is P(78.3 < X-bar < 85.1)?

Explanation / Answer

a)from CTL sampling distribution of X-bar is approximately normal

with mean =80

and std error =std deviation/(n)1/2 =14/(49)1/2 =2

b)

as z score =(X-mean)/std deviaiton

hence P(Xbar>83)=1-P(Xbar<83)=1-P(Z<(83-80)/2) =1-P(Z<1.5)=1-0.9332 =0.0668

c)

P(Xbar<75.8)=P(Z<(75.8-80)/2)=P(Z<-2.1)=0.0179

d)

P(78.3<Xbar<85.1)=P((78.3-80)/2<Z<(85.1-80)/2)=P(-0.85<Z<2.55)=0.9946-0.1977)=0.7970

please revert for any explanation required,

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