*assume normal distribution for all data and Simple random samples. Energy drink

Question

*assume normal distribution for all data and Simple random samples. Energy drinks are supposed to contain 250mL of drink. Standard deviation of volume is sigma=0.4mL. A sample of 5 cans is inspected each hour for process control purposes. The mean and standard deviation are 250ml and 0.1788mL for the sample, respectively. a- Make a sketch of the normal curve for a single can. Add the norma l curve for the mean of a SimpleRandom Sample of 5 cans on the same sketch. B - what is the probability that the volume of a single randomly chosen can differs from the target value by 0.1ml or more? c- what is the probability that the mean volume of a SRS of 5 cans differs from the target value by 0.1mL or more?

Textbook gives answer for B as P=0.0124 and for c as P is essentially 0.. Please provide solution supporting these answers.

Explanation / Answer

Data given:

Mean, m = 250

Standard Deviation, S = 0.4

Standard error, SE = 0.178

Sample size, n = 5

(b)

Calculating z-score:

z = (X-m)/S = 1/0.4 = 2.5

The corresponding right tailed p-value for this z-score is:

p = 0.00621

Since this is a two tailed test, so the p-value is:

p = 0.00621*2 = 0.0124

(c)

Calculating z-score:

z = (X-m)/S = 1/0.178 = 5.618

The corresponding right tailed p-value for this z-score is:

p < 0.00001

Since this is a two tailed test, so the p-value is:

p < 0.00002

Thus we can say that the p-value is essentially zero.

Hope this helps !

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