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Free_Kalibri [48]
2 years ago
9

Answer the following questions and round your answers to 2 decimal places. 84% of all Americans live in cities with population g

reater than 50,000 people. If 50 Americans are selected at random, Find the probability that Exactly 42 of them live in cities with population greater than 50,000 people.
Mathematics
1 answer:
nignag [31]2 years ago
4 0

Answer:

15.23% probability that exactly 42 of them live in cities with population greater than 50,000 people.

Step-by-step explanation:

For each American, there are only two possible outcomes. Either they live in cities with population greater than 50,000 people. Or they do not. The probability of a person living in a city with population greater than 50,000 people is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

84% of all Americans live in cities with population greater than 50,000 people.

This means that p = 0.84

If 50 Americans are selected at random, Find the probability that Exactly 42 of them live in cities with population greater than 50,000 people.

This is P(X = 42) when n = 50. So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 42) = C_{50,42}.(0.84)^{42}.(0.16)^{8} = 0.1523

15.23% probability that exactly 42 of them live in cities with population greater than 50,000 people.

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Answer:

Step-by-step explanation:

Hello!

The researcher suspects that the battery life between charges for the Motorola Droid Razr Max differs if its primary use is talking or if its primary use is for internet applications.

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Assuming that both variables have a normal distribution X₁~N(μ₁;σ₁²) and X₂~N(μ₂; σ₂²)

The parameters of interest are σ₁² and σ₂²

a) They want to test if the population variance of the duration time of the battery when the primary usage is for talking is greater than the population variance of the duration time of the battery when the primary usage is for internet applications. Symbolically: σ₁² > σ₂² or since the test to do is a variance ratio: σ₁²/σ₂² > 1

The hypotheses are:

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b) I've already calculated the sample standard deviations using a software, just in case I'll show you how to calculate them by hand:

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For the first sample:

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I hope this helps!

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