Question

Table C4-2: Volume, Frequency, and Charge for Wholesale Nets Sold
Volume Sold	Frequency (f)	Amount Charged (x)	x*f	Amount Charged
1	20	$3.00	$60.00	$1,455.90
2	38	$6.00	$228.00	$1,162.91
3	53	$9.00	$477.00	$339.78
4	45	$12.00	$540.00	$9.86
5	40	$14.00	$560.00	$243.64
6	13	$16.00	$208.00	$259.52
7	5	$18.00	$90.00	$209.18
8	36	$20.00	$720.00	$2,581.45
	250		$2,883.00	$6,262.24
		Mean	11.53
		Standard Deviation	5.00

3. Lee knows that she sometimes ends up with cracked or broken shells (defects) from her suppliers (independently contracted shell collectors). She decides it’s important to get a feel for the likelihood (probability) of finding defects so that she can be more informed before talking to her suppliers about the problem with the defects and related cost. She plans to randomly check 20 shells from each box to look for defects.
a. If she finds that 10% of the shells in a box are defective (cracked or broken), how likely is it that the sample of 20 from the next box she checks will have at least 3 defects? How likely is it that the sample of 20 from the next box she checks will have no more than one defect? and and Lee decides that she will only accept the boxes of shells from her suppliers if she finds that no more than 5% of the shells are defective. Thus, if she receives a box of shells that contains no more than 5% defective shells, she will consider it “good”, and a box with more than 5% defective shells will be considered “bad” and given back to the supplier. Lee checks 20 shells from all of the boxes she receives and decides that even if she finds one defective shell in the sample of 20 shells, she will send it back to the suppliers. If she does this, what is the likelihood (probability) that a “good” box (specifically, a box that has exactly 5% defective shells) will be sent back to the suppliers. Interpret the number, considering whether or not this is a fair practice by Lee.

Answer 1