Question

In a city,$46$ percent of the population favor the incumbent, Dawn Morgan, for mayor. A simple random sample of $500$is taken. Using the continuity correction factor, find the probability that at least $250$favor Dawn Morgan for mayor.

Short answer

The probability that at least $250$ favor Dawn Morgan for mayor is$0.0403$

Step-by-step solution

Given information 

Given in the question that, In a city, $46$ percent of the population favor the incumbent, Dawn Morgan, for mayor. A simple random sample of $500$ is taken.

Explanation

According to the supplied points, sample size $n$is $500$, probability of favor is $0.46$. To find the probability that at least$250$favor Dawn Morgan for mayor, use the Ti-83 calculator. For this, click on $2^{\text{nd}}$, then DISTR, and then scroll down to the binomcdf option and enter the provided details. After this, click on ENTER button of a calculator to have the wanted result. The screenshot is given below:

Thus, the probability that at least$250$favor Dawn Morgan for mayor is:

$=1-.9597$

$=0.0403$

Final answer

The probability that at least$250$ favor Dawn Morgan for mayor is$0.0403$