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3 years ago

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The probability a randomly selected household owns corporate stock is 0.54. The probability a randomly selected household has no

Internet access is 0.3. Assume whether a randomly selected household owns corporate stock is independent of whether the household has no Internet access. What is the probability a randomly selected household has no Internet access given the household owns corporate stock

1 answer:

34kurt3 years ago

8 0

Answer:

30% probability a randomly selected household has no Internet access given the household owns corporate stock

Step-by-step explanation:

I am going to say that we have two events.

Event A: Owning corporate stock. So P(A) = 0.54.

Event B: Having no internet access. So P(B) = 0.3.

Since they are independent events, we can apply the conditional probability formula, which is:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probabilitty of event B happening given that A happened. We want to find this.

$P(A \cap B)$ is the probability of both events happening.

Since they are independent

$P(A \cap B) = P(A)P(B) = 0.54*0.3$

So

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.54*0.3}{0.54} = 0.3$

30% probability a randomly selected household has no Internet access given the household owns corporate stock

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Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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Problems of normal distributions can be solved using the z-score formula.

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

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Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

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