In: Statistics and Probability
Data Below represent a sample. What is the probability of the population mean to be above 263.1?
Please include Excel Calculations.
Strength | ||||||
234.4 | 253.2 | 259 | 253.9 | 209.6 | 251.4 | 247.5 |
248.6 | 254.6 | 229.7 | 264.8 | 240.4 | 271.6 | 246 |
245.9 | 270.3 | 278.9 | 252 | 241.7 | 261.6 | 253.9 |
278.6 | 263 | 288.6 | 294.6 | 280.5 | 256.8 | 233.1 |
270.9 | 242.7 | 266.1 | 250.6 | 281.6 | 254.4 | 241.9 |
248.2 | 271.4 | 254.9 | 235.3 | 272.3 | 269.5 | 257.5 |
296.8 | 270.6 | 266.6 | 263.6 | 243.6 | 251.9 | 278.3 |
First we will find the mean and standard for given data
Create the following table.
data | data-mean | (data - mean)2 |
234.4 | -23.8224 | 567.50674176 |
253.2 | -5.0224 | 25.22450176 |
259 | 0.7776 | 0.60466176 |
253.9 | -4.3224 | 18.68314176 |
209.6 | -48.6224 | 2364.13778176 |
251.4 | -6.8224 | 46.54514176 |
247.5 | -10.7224 | 114.96986176 |
248.6 | -9.6224 | 92.59058176 |
254.6 | -3.6224 | 13.12178176 |
229.7 | -28.5224 | 813.52730176 |
264.8 | 6.5776 | 43.26482176 |
240.4 | -17.8224 | 317.63794176 |
271.6 | 13.3776 | 178.96018176 |
246 | -12.2224 | 149.38706176 |
245.9 | -12.3224 | 151.84154176 |
270.3 | 12.0776 | 145.86842176 |
278.9 | 20.6776 | 427.56314176 |
252 | -6.2224 | 38.71826176 |
241.7 | -16.5224 | 272.98970176 |
261.6 | 3.3776 | 11.40818176 |
253.9 | -4.3224 | 18.68314176 |
278.6 | 20.3776 | 415.24658176 |
263 | 4.7776 | 22.82546176 |
288.6 | 30.3776 | 922.79858176 |
294.6 | 36.3776 | 1323.32978176 |
280.5 | 22.2776 | 496.29146176 |
256.8 | -1.4224 | 2.02322176 |
233.1 | -25.1224 | 631.13498176 |
270.9 | 12.6776 | 160.72154176 |
242.7 | -15.5224 | 240.94490176 |
266.1 | 7.8776 | 62.05658176 |
250.6 | -7.6224 | 58.10098176 |
281.6 | 23.3776 | 546.51218176 |
254.4 | -3.8224 | 14.61074176 |
241.9 | -16.3224 | 266.42074176 |
248.2 | -10.0224 | 100.44850176 |
271.4 | 13.1776 | 173.64914176 |
254.9 | -3.3224 | 11.03834176 |
235.3 | -22.9224 | 525.43642176 |
272.3 | 14.0776 | 198.17882176 |
269.5 | 11.2776 | 127.18426176 |
257.5 | -0.7224 | 0.52186176 |
296.8 | 38.5776 | 1488.23122176 |
270.6 | 12.3776 | 153.20498176 |
266.6 | 8.3776 | 70.18418176 |
263.6 | 5.3776 | 28.91858176 |
243.6 | -14.6224 | 213.81458176 |
251.9 | -6.3224 | 39.97274176 |
278.3 | 20.0776 | 403.11002176 |
Find the sum of numbers in the last column to get.
So standard deviation is
As sample size is more than 30, we assume that distribution is normal as per central limit theorem
Now we need to find
As distribution is normal we can convert x to z and using excel formula we get.