A normally distributed population with mean of 46.2 and standard deviation 1.7. What is the probability if you draw a sample of size 25 from this population that the sample mean would be between 46 and 47?

First you need the Std Error of the mean value, a measure of the dispersion of that mean value.

SE = sample std deviation / sqrt (sample size)
= 100 / sqrt (64)
= 100 / 8
= 12.5

Then we use a figure for the number of std errors either side of the mean value, which make up a 95 % confidence interval. This is ± 1.96 std errors, from tables of the Normal Distribution.

So the confidence interval is

350 ± 1.96 * 12.5 or

374.5 to 325.5
.

First you need the Std Error of the mean value, a measure of the dispersion of that mean value.

SE = sample std deviation / sqrt (sample size)
= 8 / ? 64
= 1

Then we use a figure for the number of std errors either side of the mean value, which make up a 99 % confidence interval. This is ± 2.58 std errors, from tables of the Normal Distribution.

So the confidence interval is

125 ± 2.58 * 1 or

127.58 to 122.42
.

About 5.23. If this is homework, be sure to show your work.

About 19.7

Population size:4
Mean (?): 23.45
Standard deviation (?): 4.5986411036305

For a sample this smaller size there are two std deviations. Sample std deviation s(n-1) = 0.550, and population std deviation s(n) = 0.541

If you mean the standard deviation, there are two shifted keys on the third row marked with a lower-case Greek sigma. sigma_xn is the population standard deviation and sigma_xn-1 is the sample standard deviation.

Example: Enter the following x variables, and determine the sample and population standard deviations.
x = {1,2,3}

• Press [DATA] and begin to enter the data as indicated into the L1, L2 or L3 lists. To input a data point, type the value and press [ENTER]. Press the down arrow key to move on to the next data point.
• Press [2nd], [STAT], and then choose 1-VAR.
• For the "DATA" option, choose the listname the data is stored in (L1, L2 or L3). For the "FRQ" option, choose "ONE" since this data does not include a frequency list.
• Arrow down to "CALC" and press [ENTER].
  
  Answers should be as follows:
  3:Sx (Sample Standard Deviation) = 1
  4:sx (Population Standard Deviation) = 0.816497
• Press [2nd] [MODE] to exit STAT mode.

Yes. The sample standard deviation is 2nd [sigma x n-1] and the population standard deviation is 2nd [sigma x n].

64 62 52 50 70 60 55 20 25 48 35 55 55 47 64 42 36 50 30 53 51 63 58 50 60 54 33 48 40 76 61 46 65 65 15 45 58 40 64 18 33 40 64 18 33 40 48 9 38 41

Highest value observed: 76
Lowest Value: 9
Standard deviation from the ungrouped data: 15.25
Frequency:
Mean: 46.94
Standard deviation from grouped data: 15.40