Question

Manufacturing companies strive to maintain production consistency, but it is often difficult for outsiders to tell whether they have succeeded. Consider a company that makes a certain brand of candy claims that 8% of the candies it produces are yellow and that bags are packed randomly. Their production controls can be checked by sampling bags of candies. Suppose bags containing about 300 candies are opened and the proportion of yellow candies is recorded.

**Question: It's appropriate to use normal model because
np=______ and nq=_______**

**Question: About 68% of the bags will have between _____%
and ______% orange candles.**

**Question: About 95% of the bags will have between _____%
and _______% orange candles.**

**Question: About 99.7% of the bags will have between
______% and ______% orange candles.**

Answer #1

P(yellow candy), p = 0.08

q = 1 - p = 0.92

Sample size, n = 300

np = 300x0.08 = **24**

nq = 300x0.92 = **276**

np and nq > 10. So, it is appropriate to use normal model.

Mean, of sample proportion = 8

Standard deviation of sample proportion =

=

= 0.0157

According to the empirical rule, 68%, 95% and 99.7% of the data values lie within 1, 2 and 3 standard deviations of mean.

About 68% of the bags will have between 8-0.0157 =
**7.9843**% and 8+0.0157 = **8.0157**%
yellow candies.

Question: About 95% of the bags will have between 8-2x0.0157 =
**7.9687**% and 8+2x0.0157 = **8.0313**%
yellow candies.

Question: About 99.7% of the bags will have between 8-3x0.0157 =
**7.9529**% and 8+3x0.0157 = **8.0471**%
yellow candies.

Manufacturing companies strive to maintain production
consistency, but it is often difficult for outsiders to tell
whether they have succeeded. Consider a company that makes a
certain brand of candy claims that 8% the candies it produces are
yellow and that bags are packed randomly. Their production controls
can be checked by sampling bags of candies. Suppose bags containing
about 300 candies are opened and the proportion of yellow candies
is recorded. Complete parts a through c.
a) Explain why...

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INNOVATION
Deep Change: How Operational Innovation Can Transform Your
Company
by
Michael Hammer
From the April 2004 Issue
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8.95
In 1991, Progressive Insurance, an automobile insurer based in
Mayfield Village, Ohio, had approximately $1.3 billion in sales. By
2002, that figure had grown to $9.5 billion. What fashionable
strategies did Progressive employ to achieve sevenfold growth in
just over a decade? Was it positioned in a high-growth industry?
Hardly. Auto insurance is a mature, 100-year-old industry...

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