4 Vitamin E tablets 1 point possible (graded) Johnson and Johnson is a American

Question

4 Vitamin E tablets 1 point possible (graded) Johnson and Johnson is a American pharmaceutical company which produces tablets with Vitamin E in it. In the laboratories they took a random sample from a day's production and measured the amount of vitamin E the tablets contained in percent. These were the results from the six tablets they picked out that day: 23.5%, 22.4%, 23.0%, 21.9%, 22.6%, 22.8%, (Note: please work in "Percent, 96" which means you do not have to convert to 0.235,0.224, etc.) It is known that the amount of vitamin E tables is normally distributed with standard deviation equal to 0.55%. (Note: please work in "Percent, %, which means you do not have to convert to 0.0055) Using the sample information, determine a 95% confidence interval for the mean amount of vitamin E in the tablets of the population of the tablets produced that day. 122.26, 23.14 122.52,22.88 120.64, 24.76 122.66, 22.74 You have used 0 of 1 attempt

Explanation / Answer

Solution:
Mean of the sample = (23.5+22.4+23+21.9+22.6+22.8)/6 = 136.2/6 = 22.7

and population standard deviation = 0.55
and Standard error = 0.55/sqrt(6) = 0.2245
So Confidence interval can be calculated as
mean +/- Zalpha/2 *standard error
Here alpha=0.05 and alpha/2 = 0.025 and Zalpha/2 = 1.96
22.7+/-1.96*0.2245
22.7 - 0.44002 to 22.7+0.44002
22.26 to 23.14

So its confidence interval is (22.26,23.14) and its answer is A.

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