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 Dan Morgan for mayor is$0.0403$

Step-by-step solution

Given information

The population of $46$percent in the city favors the incumbent. And a simple random sample of $500$is taken.

Explanation

The random variable $X$ is a binomial distribution,

Therefore,

$X~B(n,p)$

Here $X$is the number that favor the incumbent.

$n=500$simple random sample

$p=0.46$the population favor the incumbent.

The formula for the mean deviation is $\mu =np$

And for standard deviation is $\sigma =\sqrt{npq}$.

The random variable for the normal distribution is$Y$.

$Y~N(230,11.1445)$

Using normal cumulative distribution function calculator, that the probability at least $250$favor Dawn Morgan for mayor is $0.04$.

Explanation

Using binomcdf calculator, that the probability at least 250 favor Dawn Morgan for mayor is$1-0.9597=0.0403$.

Final answer

The probability that at least $250$favor Dawn Morgan for mayor is $0.04$.