In an election, suppose that 60% of voters support the incumbent candidate. If we poll 193 of these voters at random, the probability distribution for the proportion of the polled voters that support the incumbent candidate can be modeled by the normal distribution pictured below. Complete the boxes accurate to two decimal places.

The probability distribution for the proportion of polled voters that support the incumbent candidate can be modeled by a normal distribution. In this case, we are told that 60% of voters support the incumbent candidate.

To find the probability distribution for the proportion of the polled voters that support the incumbent candidate, we need to use the following formula:

mean = p
standard deviation = sqrt((p * (1 - p)) / n)

where p is the proportion of voters that support the incumbent candidate (in this case, 0.60) and n is the sample size (in this case, 193).

To calculate the mean, we simply multiply the proportion by the sample size:

mean = 0.60 * 193 = 115.8

To calculate the standard deviation, we need to use the formula:

standard deviation = sqrt((0.60 * (1 - 0.60)) / 193)

standard deviation ≈ sqrt((0.60 * 0.40) / 193)

standard deviation ≈ sqrt(0.24 / 193)

standard deviation ≈ sqrt(0.00124478)

standard deviation ≈ 0.0353

Therefore, the mean of the probability distribution is approximately 115.8 and the standard deviation is approximately 0.0353.

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