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In a city, 46percent of the population favor the incumbent, Dawn Morgan, for mayor. A simple random sample of500is taken. Using the continuity correction factor, find the probability that at least 250 favor Dawn Morgan for mayor.

Short Answer

Expert verified

The probability that at least 250favor Dan Morgan for mayor is0.0403

Step by step solution

01

Given information

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

02

Explanation

The random variable X is a binomial distribution,

Therefore,

X~B(n,p)

Here Xis the number that favor the incumbent.

n=500simple random sample

p=0.46the population favor the incumbent.

The formula for the mean deviation is μ=np

And for standard deviation is σ=npq.

The random variable for the normal distribution isY.

Y~N(230,11.1445)

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

03

Explanation

Using binomcdf calculator, that the probability at least 250 favor Dawn Morgan for mayor is10.9597=0.0403.

04

Final answer

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

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