<p><br />The average price of cell phones manufactured by Ahmadi, Inc. is $98 wi

Question

<p><br />The average price of cell phones manufactured by Ahmadi, Inc. is $98 with a standard&#160;deviation of $12. Furthermore, it is known that the prices of the cell phones manufactured&#160;by Ahmadi are normally distributed.</p>
<p>a. What percentage of cell phones produced by Ahmadi, Inc. will have prices of at least&#160;$120.20?&#160;</p>
<p>b. Cell phones with prices of at least $81.80 will get a free gift. What percentage of the cell&#160;phones will be eligible for the free gifts?&#160;</p>
<p>c. What are the minimum and maximum values of the middle 95% of cell phone prices?</p>

Explanation / Answer

Given X~Normal(=98, s=12)

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(a) P(X>=120.2) = P((X-)/s >= (120.2-98)/12)

=P(Z>= 1.85)

= 0.0322 (check standard normal table)

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(b) P(X>= 81.8) = P(Z>= (81.8-98)/12)

=P(Z >= -1.35)

= 0.9114(check standard normal table)

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(c) Given a=0.05, Z(0.025)=1.96 (check standard normal table)

xbar ± Z*s

--> 98 ± 1.96*12

--> ( 74.48, 121.52)

So min=74.48

max=121.52

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