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Finger [1]
3 years ago
14

Suppose that 76% of Americans prefer Coke to Pepsi. A sample of 80 was taken. What is the probability that at least seventy perc

ent of the sample prefers Coke to Pepsi?
A. 0.104
B. 0.142
C. 0.896
D. 0.858
E. Can not be determined.
Mathematics
1 answer:
Anastasy [175]3 years ago
4 0

Answer:

C. 0.896

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 80, p = 0.76

So

E(X) = np = 80*0.76 = 60.8

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{80*0.76*0.24} = 3.82

What is the probability that at least seventy percent of the sample prefers Coke to Pepsi?

0.7*80 = 56.

This probability is 1 subtracted by the pvalue of Z when X = 56. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{56 - 60.8}{3.82}

Z = -1.26

Z = -1.26 has a pvalue of 0.1040.

1 - 0.1040 = 0.8960

So the correct answer is:

C. 0.896

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scoray [572]

Answer:

129.996 cubic feet

Step-by-step explanation:

Assuming that the barrel is a perfect cylinder, we can use the formula to find the volume:

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First, we have to find the radius, which is:

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A manager finds a moderate negative correlation between the number of computer sales and the number of microwave sales in his st
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The true statement is the correlation is most likely due to a lurking variable.

<h3>What is negative correlation?</h3>

Correlation is a statistical measure used to measure the relationship that exists between two variables. Negative correlation is when there is an inverse relationship between the two variables. If one variable increases, the other variable decreases.

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a rectangle measures 3 yards by 4 feet what is the perimeter of the rectangle in inches show your work please
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Length: 3 yds. 36 in= 1 yd; 108 in.=3 yds
Width: 4 ft. 12 in=1 ft.; 48 in= 4 ft.
Sinve there are two lengths and widths in a rectangle, I like to multiply them both by 2 and add up the results. You also get the same answer when you add everything up twice. My answer is 312 in.
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3.35 is bigger then 3.345
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