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Answer:
24 munchkins.
Step-by-step explanation:
Let C be the number of chocolate and D be number of glazed donut holes in the original box.
We are told if Jacob ate 2 chocolate munchkins, then 1/11 of the remaining Munchkins would be chocolate. We can represent this information as:
We are also told if he instead added 4 glazed Munchkins to the original box, 1/7 of the Munchkins would be chocolate. We can represent this information as:
Upon substituting C's value from equation (2) in equation (1) we will get,
Let us have a common denominator on right side of equation.
Multiplying both sides of our equation by 7, we will get,
Multiplying both sides of our equation by 11, we will get,
Therefore, the total number of Munchkins in original box is 24.
Answer:
a) The 99% confidence interval is from 14.8% to 23.2%.
b) The confidence interval tells us that the true proportion of mislabeled is within 14.8% and 23.2%, with a 99% confidence. In other words, if we take samples of the same size, 99% of the samples will have a proportion within 0.148 and 0.232.
c) The confidence interval calculation take into account the sample size, so the width (or precision) of the interval depends on the sample size.
The only criticism that could be analyzed is to see if the sample is representative of the population.
Step-by-step explanation:
a) We have to calculate a 99% confidence interval for the proportion.
The sample proportion is p=0.19.
The standard error of the proportion is:
The critical z-value for a 99% confidence interval is z=2.576.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 99% confidence interval for the population proportion is (0.148, 0.232).