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Sampling Distributions For Questions 6 - 8, let the random variable X follow a Normal distribution...

Sampling Distributions
For Questions 6 - 8, let the random variable X follow a Normal distribution with variance σ2 = 625.
Q6. A random sample of n = 50 is obtained with a sample mean, X-Bar of 180.
What is the probability that population mean μ is greater than 190?
a. What is Z-Score for μ greater than 190 ==>
b. P[Z > Z-Score] ==>
Q7. What is the probability that μ is between 198 and 211?
a. What is Z-Score1 for μ greater than 198 ==>
b. What is Z-Score2 for μ less than 211 ==>
c. P[Z-Score1 < Z < Z-Score2] ==>
Q8. A second random sample of n = 75 is obtained, again with a sample mean X-Bar of 180. What is the probability that μ is between 177 and 190?
a. What is Z-Score1 for μ greater than 177 ==>
b. What is Z-Score2 for μ less than 190 ==>
c. P[Z-Score1 < Z < Z-Score2] ==>
math   Statistics-And-Probability   
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Answer #1

Here, in the question you have given x-bar and variance.

but in questions you asked the probability of mu. Instead it should be probability of x.

Following are the answers for your questions with X,

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