Question

Use the store's annual mean and standard deviation for your analysis. Determine the probability that on any1 given day the main street store would have sales

a) greater than 50 atlas tires

b) fewer than 30 atlas tires

c) between 40 atlas tires and 80 atlas tires

Month	Main Street Location
20xx	Atlas Tires	Continental
January	52	12
February	38	22
March	27	26
April	14	0
May	26	0
June	14	8
July	8	16
August	14	4
September	32	12
October	0	24
November	12	0
December	8	18

Main Street Stats
Atlas Tires							Continental
Mean	Median	Mode	Deviation	Squared Deviation	Quartiles		Mean	Median	Mode	Deviation	Squared Deviation	Quartiles
20.4166667	14	14			1st	11	11.83333333	12	0			1st	3
					2nd	14						2nd	12
	0	0	-20.4167	416.8403	3rd	28.25		0	0	-11.8333	140.0278	3rd	19
	8	8	-12.4167	154.1736	4th	52		0	0	-11.8333	140.0278	4th	26
	8	8	-12.4167	154.1736				0	0	-11.8333	140.0278
	12	12	-8.41667	70.84028				4	4	-7.83333	61.36111
	14	14	-6.41667	41.17361				8	8	-3.83333	14.69444
	14	14	-6.41667	41.17361				12	12	0.166667	0.027778
	14	14	-6.41667	41.17361				12	12	0.166667	0.027778
	26	26	5.583333	31.17361				16	16	4.166667	17.36111
	27	27	6.583333	43.34028				18	18	6.166667	38.02778
	32	32	11.58333	134.1736				22	22	10.16667	103.3611
	38	38	17.58333	309.1736				24	24	12.16667	148.0278
	52	52	31.58333	997.5069				26	26	14.16667	200.6944
Total	245			2434.917			Total	142			1003.667
Annual Range	Standard Deviation		Coefficient of Variation				Annual Range	Standard Deviation		Coefficient of Variation
0-52	14.24464		69.77%				0-26	9.14543		77.29%

Answer 1

a) greater than 50 atlas tires

z = (x - µ)/σ = (50 - 20.42)/14.24464 = 2.08

P (z > 50) = 0.0189

b) fewer than 30 atlas tires

z = (x - µ)/σ = (30 - 20.42)/14.24464 = 0.67

P (z < 30) = 0.7494

c) between 40 atlas tires and 80 atlas tires

z = (x - µ)/σ = (40 - 20.42)/14.24464 = 1.37

P (z = 40) = 0.9154

z = (x - µ)/σ = (80 - 20.42)/14.24464 = 4.18

P (z = 80) = 1.0000

Required probability = 1.0000 - 0.9154 = 0.0845