Problem

In an election, suppose that $35 \%$ of voters support a school levy increase. If we poll 104 of these voters at random, the probability distribution for the proportion of the polled voters that support a school levy increase can be modeled by the normal distibution pictured below. Complete the boxes accurate to two decimal places

Solution

Step 1 :This problem is about the normal distribution. The mean of the distribution is the actual proportion of voters that support the school levy increase, which is 0.35.

Step 2 :The standard deviation can be calculated using the formula for the standard deviation of a sample proportion, which is \(\sqrt{p*(1-p)/n}\), where p is the proportion of the population that has the characteristic of interest (in this case, supporting the school levy increase), and n is the sample size.

Step 3 :Given that p = 0.35 and n = 104, we can substitute these values into the formula to calculate the standard deviation.

Step 4 :After calculation, the standard deviation is approximately 0.046770717334674264.

Step 5 :Rounding to two decimal places, the standard deviation is approximately 0.05.

Step 6 :Final Answer: The mean of the distribution is 0.35 and the standard deviation is approximately \(\boxed{0.05}\).

From Solvely APP
Source: https://solvelyapp.com/problems/18346/

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