S is the standard deviation of the sample Previous answer wa

**S is the standard deviation of the sample.

Previous answer was incorrect.

Y1, Y2, ... Y9 is a random sample from normal population with mu = 5 and unknown sigma^2. What is the probability that Y is within 1/3 S of the population mean?} ** Y is the sample mean}. **S is the standard deviation of the sample. Previous answer was incorrect.

Solution

When Y1, Y2, ...Y9 are random samples from normal population

Expected value of mean of Y

i.e. E(Y bar ) = 5

Y bar lies within 1/3 S of population mean :

s = sigma/rtn = sigma/3

s/3 = sigma/9

Hence prob for y bar to lie within 1/3 s = P(|y bar-5|<=sigma/9)

= P(|Z|<= 1/9)

=P(|std normal variate|<=0.111

From std normal distribution table we find

Prob = 0.0438+0.0438(on either side)

   = 0.0876