1. Consider a sample, X1,..., Xn , of normally distributed random variables with mean u and variance o? = 9. (a) If n=16, what is the probability that |x-uC0.3? (b) What is this probability when n=81?

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Can you please solve both of the questions and please show the work for both of them as well as can you please show the r code.

1. Consider a sample, X, ..., Xn , of normally distributed random variables with mean u and variance o?
= 9.
(a) If n=16, what is the probability that |x-u|<0.3?
(b) What is this probability when n=81?
Transcribed Image Text:1. Consider a sample, X, ..., Xn , of normally distributed random variables with mean u and variance o? = 9. (a) If n=16, what is the probability that |x-u|<0.3? (b) What is this probability when n=81?
3. A sample of 58 data observations has a sample mean of 0.0328. If an experimenter wishes to use a
"known" value o=0.015 for the population standard deviation, construct an appropriate 95%
confidence interval for the population mean µ.
Transcribed Image Text:3. A sample of 58 data observations has a sample mean of 0.0328. If an experimenter wishes to use a "known" value o=0.015 for the population standard deviation, construct an appropriate 95% confidence interval for the population mean µ.
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