1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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

You might be interested in
4x-1/y -3=2 solve for y
Taya2010 [7]
This is the answer it was easier just to write it out

7 0
3 years ago
D says reflection across y=x please help
antoniya [11.8K]
The answer should be A.
7 0
3 years ago
Solve: 25 - 5x = 80<br>A. 8/3<br>B. -11<br>C. 4<br>D. 21
natita [175]
-5x=80-25
-5x=55
x=-11
8 0
3 years ago
Read 2 more answers
In a standard normal distribution 95% of the data is within +/- _______standard deviations of the mean.
raketka [301]
Your answer is 2 okay
8 0
3 years ago
Read 2 more answers
A 120 120 -volt battery is connected to a circuit with 30 30 ohms of resistance. The current in amperes c c flowing through the
coldgirl [10]

Answer:

just divide 120 divided by 30 is 4 I know it right bc I had the same question on into math if thats what you were on

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • a ferris wheel rotates around in 30 seconds. the maximum height above theground is 55 feet and the minumum height above the grou
    9·2 answers
  • charlies car used 3.62 galons of gas for 84 miles drive. how many miles to the gallon did his car get?
    12·1 answer
  • Nigel is one and one half as tall as his brother who is three and three fourths feet tall. How tall is Nigel?
    5·1 answer
  • A problem states: "There are 7 more girls than boys in a class. There are 23 students in the class in all. How many girls are th
    11·1 answer
  • A park ranger standing in a 146-foot lookout tower sees the beginning of a forest fire. she measures the angle of depression fro
    8·1 answer
  • PLZ HURRY IT'S URGENT!!!!!
    12·1 answer
  • Julio ​says, "If you subtract 16 from my number and multiply the difference by −6​, the result is −138​." What is Julio​'s ​numb
    7·1 answer
  • Find the point on the terminal side of θ = three pi divided by four that has a y coordinate of 1. Show your work for full credit
    7·1 answer
  • Patricia tiene $80.000 sólo en billetes de $5.000, Camila tiene $60.000 sólo en billetes de $2.000 y Andrea tiene $120.000 sólo
    6·1 answer
  • Brainliest 5 stars and thank you! (correct answers only)<br><br> What is the qoutient?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!