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antcobra
17.02.2020 •
Mathematics
A consumer group is interested in estimating the proportion of packages of ground beef sold at a particular store that have an actual fat content exceeding the fat content stated on the label. How many packages of ground beef should be tested to estimate this proportion to within 0.05 with 95 % confidence?
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Ответ:
And rounded up we have that n=385
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by
and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
And on this case we have that
and we are interested in order to find the value of n, if we solve n from equation (a) we got:
We assume that the estimated proportion for this case is
since we don't have prior information.
And replacing into equation (b) the values from part a we got:
And rounded up we have that n=385
Ответ:
40 miles/ 1 hour
Step-by-step explanation:
Because the GPS will take Lanny 1 hour to travel 40 miles so u have to divide 40 miles by 1 hour.