(8 marks) The average price of cell phones manufactured by Apple, Inc. is $98 wi

Question

(8 marks) The average price of cell phones manufactured by Apple, Inc. is $98 with a standard deviation of $12. Furthermore, it is known that the prices of the cell phones manufactured by Apple are normally distributed. 4. What percentage of cell phones produced by Apple, Inc. will have prices of at least $120.20? Cell phones with prices of at least 81.80 will get a free gift. What percentage of the cell phones will be eligible for the free gift? what are the minimum and the maximum values of the middle 95% of cell phone prices? If 7,218 of the Apple cell phones were priced at least $119.00, how many cell phones were produced by Apple, Inc.? a. b. c, d.

Explanation / Answer

mean = 98
std. dev. = 12

a)
P(X >= 120.2) = P(z > (120.2 - 98)/12) = P(z > 1.85) = 0.0322

b)
P(X >= 81.8) = P(z > (81.8 - 98)/12) = P(z > -1.35) = 0.9115

91.15%

c)

d)

P(X >= 119) = P(z > (119 - 98)/12) = P(z > 1.75) = 0.04

n*p = 7218
n = 7218/0.04 = 180450

n 1 mu 98.00 Confidence Interval xbar +/- ME sigma 12 Lower bound 74.48043 SE = sigma/sqrt(n) 12.0000 Upper bound 121.51957 CI 95% Confidence Interval (74.4804 , 121.5196 ) z-value 1.9600 ME = z*SE 23.5196

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