engths are normally destributed You randomly select 43 boards and ind that the m

Question

engths are normally destributed You randomly select 43 boards and ind that the mean length is 108 12 inches Complete parts (a) through (c) EE Click the icon to view page 1 of the standard normal table Ea Clokte icon to view page 2 ofthe standard normal table s 108 12 inches or more? 15738 (Round to four decimal places as needed) ) Using your answer tom part (a) what do you think ofthe seller's dam? be considered unusual because, & the seller's claien is true, the probutbility of obtaining this sample mean is (c) Assuming the seler's claim is true, board with a length of 108 12 inches? Why or why not? ae 12 ?-thin 2 standard deviations of the mean for anindvdual board O Type here to

Explanation / Answer

First we summarize the data given in the question:

Size, n = 43

Sample Mean, m = 108.12

Standard deviation, S = 0.5

Calculate z-statistic using formula:

z = (m-108)/(S/(n^0.5)) = (108.12-108)/(0.5/(43^0.5)) = 1.5738

The p-value for this z-value is:

p = 0.0577

So probability that sample mean length is 108.12 " or more is 0.0577

(b)

Seller claims that mean length is 108" or more, but not less than that.

So,

Seller's claim appears to be false, The sample mean should not be considered unusual because if the seller's claim is true, probability of obtaining this sample is 0.0577 which is greater than significance level of 0.05

(c)

Since standard deviation is 0.5, so the correct answer is:

No, because 108.12 lies within 1 standard deviation from the mean for an individual board.

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