Data Below represent a sample. What is the probability of the population mean to be above...

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

Expert Solution

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.

orchestra answered 1 year ago

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