Question

The following are the percentages of ash content in 12 samples of coal found in
close proximity:
9.2, 14.1, 9.8, 12.4, 16.0, 12.6, 22.7, 18.9, 21.0, 14.5, 20.4, 16.9
Find the
(a) sample mean, and
(b) sample standard deviation of these percentages.

Answer 1

Answer:

we have a normally distributed population with the mean of 1- 14 and a standard deviation of 122. And were asked for the probability that a single randomly selected element X, The quality that a random list women selected element X is between 1100 and 1300. So this population is normally distributed. So we can just use our population mean and standard deviation to do the conversion. So we have the probability that is easy Is between .7 and -13 And that is basically .758 -1762, Which gives us .5818, Part B with us for the means First of samples of size 25 7 mean is 1214. The standard deviation is Until 2/5, which is 24.4. So we have an answer to part B. Let's see for us for the probability That the mean of a sample of size 25 drawn from this population is between 1100 and 1300. So we're basically going to convert that to our standard normal random variable using the example mean and standard deviation. So we have Z between 3.52 and -4.67, So see less than 3.5 took this .9998 C, less than -4.670. And we have our answer to part C.