SOLUTION: Question 1
The weight of potato chips in a medium‐size bag is stated to be 10 ounces. The amount that the
packaging machine puts in these bags is believed to have a Normal di
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-> SOLUTION: Question 1
The weight of potato chips in a medium‐size bag is stated to be 10 ounces. The amount that the
packaging machine puts in these bags is believed to have a Normal di
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Question 1148237: Question 1
The weight of potato chips in a medium‐size bag is stated to be 10 ounces. The amount that the
packaging machine puts in these bags is believed to have a Normal distribution with a mean of 10.2
ounces and a standard deviation of 0.14 ounces.
(a) What fraction of all bags sold are underweight?
(b) Some of the chips are sold in “bargain packs” of 6 bags. What is the probability that the mean
weight of the 6 bags is below the stated amount?
(c) If the production engineer wants to change the value of the mean but maintain the standard
deviation at 0.14 ounces so that at most 1.5% of all bags are underweight, how large does
the engineer need to make that mean?
Question 2
Police departments often try to control traffic speed by placing speed‐measuring machines on roads
that tell motorists how fast they are driving. Traffic safety experts must determine where machines
should be placed. In one recent test, police recorded the average speed clocked by cars driving on
one busy street close to an elementary school. For a sample of 16 speeds, it was determined that
the average amount over the speed limit for the 16 clocked speed was 11.6 mph.
Without the information of the population standard deviation, t‐distribution is used to construct the
95% confidence interval for the unknown population mean. The confidence interval ranged from
7.337 mph to 15.863 mph.
(a) What assumption is needed to construct the mentioned confidence interval? Why?
(b) Determine the sampling error and the sample standard deviation?
(c) The researchers commented that the confidence interval was too wide. With all other things
remain unchanged, what sample size is needed in order to reduce the sampling error by 60%?
(d) The researchers later found that one sample speed is mistakenly recorded. After the
correction, both the sample mean and sample standard deviation become larger. Discuss
how would this affects the mentioned confidence interval.
