Question

his Quiz: 101 pts possibl ph Your umber company has bought a machine that automalicaly hrough (c) EEB Click the icon to view page 1 of the standard normal table EEB Click the icon to view page 2 of the standard normal table (a) Assuming the seller's claim is correct, what is the probabity that the mean of the sample is 84 28 inches or more? cuts lumber. The seller of the machine claims that the machine cuts lumber to a mean length of 7 feet (84 engths are normally distributed. You randomly select 38 boards and find that the mean length is 84 28 inches Complete parts (a) inches) with Round to four decimal places as needed) tb) Using your answer from part (a), what do you think of the seller's claim? oe consdened unusual because he selers caim s rue. the probabity or oa The sellers claim appears to be The sample mean spk mean accurate (c) Assuming the seller's claim is I to have an individual board with a length of 84.28 inches? Why or why not? inaccurate Y because 84.28Wm Wmutios of the mean for an indvidual board

Answer 1

A) P($\bar x$> 84.28)

= P(($\bar x$ - $\mu$)/($\sigma/\sqrt n$) > (84.28 - $\mu$)/($\sigma/\sqrt n$))

= P(Z > (84.28 - 84)/(0.6/$\sqrt 38$)

= P(Z > 2.88)

= 1 - P(Z < 2.88)

= 1 - 0.9980

= 0.002

B) The seller' claim appears to be accurate . The sample mean should be considered unusual because, if the seller' s claim is true, the probability of obtaining this sample mean is less than 5%.

C) 84 - 2 * 0.6 = 82.8

84 + 2 * 0.6 = 85.2

N0, because 84.28 is within 2 standard deviations of the mean for an individual board.