Answer to Question #319997 in Statistics and Probability for Ali De Austria

Question

Show your solution:

1. If the population of ABM students of Malaya Integrated High School has a mean of 12.45, what

is the mean of the sampling distribution of its mean?

2. If the mean of the sampling distribution is 24.29, what is the mean of the population?

3. If a population of HUMS students of Makabayan National High School has a variance of 6.4,

what is the variance of the sampling distribution of the sample mean if the sample size is 4 and all

the possible samples are drawn with replacements?

4. If the population of STEM students of Siyensiya Stand Alone Senior High School has a standard

deviation of 9.4, what is the standard deviation of the sampling distribution of its means? The

sampling distribution was derived with sample size n=3, and all the possible samples were drawn

with replacements.

5. If the population standard deviation is 5.6, what is the population variance

Answer 1

$1:\mu _{\bar{x}}=\mu =12.45\\2:\mu =\mu _{\bar{x}}=24.29\\3:{\sigma ^2}_{\bar{x}}=\frac{\sigma ^2}{n}=\frac{6.4}{4}=1.6\\4: \sigma _{\bar{x}}=\frac{\sigma}{\sqrt{n}}=\frac{9.4}{\sqrt{3}}=5.42709\\5: \sigma ^2=5.6^2=31.36$