The package of a particular brand of rubber band says that the bands can hold a weight of 7 lbs. Suppose that we suspect this might be an overstatement of the breaking weight So we decide to take a random sample of 36 of these rubber bands and record the weight required to break each of them. The mean breaking weight of our sample of 36 rubber bands is 6.6 lbs. Assume that the standard deviation of the breaking weight for the entire population of these rubber bands is 2 lbs. Finding a random sample with a mean this low in a population with mean 7 and standard deviation 2 is very unlikely. a. True b. False

Question

Mathematics

Courtney Hill

5 November, 20:20

The package of a particular brand of rubber band says that the bands can hold a weight of 7 lbs. Suppose that we suspect this might be an overstatement of the breaking weight So we decide to take a random sample of 36 of these rubber bands and record the weight required to break each of them. The mean breaking weight of our sample of 36 rubber bands is 6.6 lbs. Assume that the standard deviation of the breaking weight for the entire population of these rubber bands is 2 lbs. Finding a random sample with a mean this low in a population with mean 7 and standard deviation 2 is very unlikely. a. True b. False

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Hoffman · Answer 1

False this value is very likely to find in this distribution

Step-by-step explanation:

With mean 7 (μ) and standad deviation (σ) 2 we can observe, value 6.6 is close to the lower limit of the interval

μ ± 0,5 σ 7 ± 1 in which we should find 68,3 % of all values

(just 6 tenth to the left)

And of course 6.6 is inside the interval

μ ± 1 σ where we find 95.7 % of th value

We conclude this value is not unlikely at all