In 1996 there was a battle in courts and in the marketplace between Intel and Di
ID: 3021719 • Letter: I
Question
In 1996 there was a battle in courts and in the marketplace between Intel and Digital Equipment Corp. abput the technology behind Intel's Pentium microprocessing chip. Digital accused Intel of willful infringement on Digital's parents. Although Digital's Alpha microprocessor chip was the fastest on the market at the time, its speed fell victim to Intel's marketing cloud. That same year, Intel shipped 76% of the microproccesor market. Suppose a random sample of n=1,000 personal computer (PC) sales is monitored and the type of microprocessor installed is recorded. Let ^p be the proportion of personal computers in the sample with a Pentium microprocessor.
A) What are the mean, standard deviation, and shape of th distribution of ^p?
B) Using th enormal approximation without the contiunity correction, what's the probability you'd draw a random sample of 1,000 PCs with a proportion of Pentium chips exceeding 80%?
C) Looking at the answer you got for part B, if you got a simple random sample with ^p > .8, would you conclude the population proportion may be higher than .76%? Why?
Explanation / Answer
A)
Here,
n = 1000
p = 0.76
Hence,
u = mean = p = 0.76 [ANSWER]
s = standard deviation = sqrt(p(1-p)/n) = 0.013505554 [ANSWER]
It is bell shaped. [ANSWER]
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b)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 0.8
u = mean = p = 0.76
s = standard deviation = sqrt(p(1-p)/n) = 0.013505554
Thus,
z = (x - u) / s = 2.961744389
Thus, using a table/technology, the right tailed area of this is
P(z > 2.961744389 ) = 0.001529508 [ANSWER]
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c)
YES, because the probability that it only occured by chance is so small, as in part b).
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