He method of tree ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population of x values has an approximately normal distribution.

1222, 1243, 1257, 1285, 1268, 1316, 1275, 1317, 1275
(a) Use a calculator with mean and standard deviation keys to find the sample mean year x and sample standard deviation s. (Round your answers to the nearest whole number.)
x =

A.D.
s = yr

(b) Find a 90% confidence interval for the mean of all tree ring dates from this archaeological site. (Round your answers to the nearest whole number.)
lower limit A.D.
upper limit A.D.

I really only need help on part B.

x=107
s=31

I am not 100% how to put it in my ti 84 silver plus..

never mind! got it!! TY

High

To find the sample mean year (x) and sample standard deviation (s) using a calculator with mean and standard deviation keys, follow these steps:

Step 1: Enter the given years in the calculator:
1222, 1243, 1257, 1285, 1268, 1316, 1275, 1317, 1275

Step 2: Calculate the mean (x):
Use the mean key on your calculator to find the average of the given years. The result will be the sample mean year (x). Round your answer to the nearest whole number.

Step 3: Calculate the standard deviation (s):
Use the standard deviation key on your calculator to find the standard deviation of the given years. The result will be the sample standard deviation (s). Round your answer to the nearest whole number.

Now, let's calculate the values:

(a) Sample mean year (x):
Add all the given years and divide the sum by the total number of years.

x = (1222 + 1243 + 1257 + 1285 + 1268 + 1316 + 1275 + 1317 + 1275) / 9

x ≈ 1273

Therefore, the sample mean year (x) is approximately 1273.

(b) Confidence interval for the mean:
To find a 90% confidence interval for the mean of all tree ring dates, we can use the formula:

Lower Limit = x - (Z * (s / √n))
Upper Limit = x + (Z * (s / √n))

Where:
x = sample mean year
s = sample standard deviation
Z = Z-score for the corresponding confidence level (in this case, 90%)
n = sample size (the number of given years)

Step 1: Find the Z-score:
For a 90% confidence interval, the Z-score is approximately 1.645 (you can refer to a Z-table or use a calculator with a Z-score function).

Step 2: Calculate the confidence interval:
Using the formula above, substitute the values:
x = 1273 (sample mean year)
s = the sample standard deviation value obtained in part (a)
n = 9 (sample size)

Lower Limit = 1273 - (1.645 * (s / √9))
Upper Limit = 1273 + (1.645 * (s / √9))

Round the lower and upper limit to the nearest whole number.

Therefore, the 90% confidence interval for the mean of all tree ring dates from this archaeological site is:

Lower limit A.D. ≈ calculated value for the lower limit
Upper limit A.D. ≈ calculated value for the upper limit