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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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Most popular questions from this chapter

Yoonie is a personnel manager in a large corporation. Each month she must review 16of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2hours. Let Χ be the random variable representing the time it takes her to complete one review. Assume Χ is normally distributed. Let x-be the random variable representing the meantime to complete the 16reviews. Assume that the 16reviews represent a random set of reviews.

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M&M candies large candy bags have a claimed net weight of 396.9g. The standard deviation for the weight of the

individual candies is 0.017g. The following table is from a stats experiment conducted by a statistics class.

RedOrangeYellowBrownBlueGreen
0.751
0.735
0.883
0.696
0.881
0.925
0.841
0.895
0.769
0.876
0.863
0.914
0.856
0.865
0.859
0.855
0.775
0.881
0.799
0.864
0.784
0.8060.854
0.865
0.966
0.852
0.824
0.840
0.810
0.865
0.859
0.866
0.858
0.868
0.858
1.015
0.857
0.859
0.848
0.859
0.818
0.876
0.942
0.838
0.851
0.982
0.868
0.809
0.873
0.863


0.803
0.865
0.809
0.888


0.932
0.848
0.890
0.925


0.842
0.940
0.878
0.793


0.832
0.833
0.905
0.977


0.807
0.845

0.850


0.841
0.852

0.830


0.932
0.778

0.856


0.833
0.814

0.842


0.881
0.791

0.778


0.818
0.810

0.786


0.864
0.881

0.853


0.825


0.864


0.855


0.873


0.942


0.880


0.825


0.882


0.869


0.931


0.912





0.887

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a. Find the mean sample weight and the standard deviation of the sample weights of candies in the table.

b. Find the sum of the sample weights in the table and the standard deviation of the sum of the weights.

c. If 465M&Ms are randomly selected, find the probability that their weights sum to at least 396.9.

d. Is the Mars Company’s M&M labeling accurate?

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