# A report describes the results of a large survey involving approximately 3500 people that was conducted for the Center for Disease Control. The sample was selected in a way that the Center for Disease Control believed would result in a sample that was representative of adult Americans. One question on the survey asked respondents if they had learned something new about a health issue or disease from a TV show in the previous 6 months. Data from the survey was used to estimate the following probabilities, where L-event that a randomly selected adult American reports learning somethlng new about a health Issue or disease from a TV show in the previous 6 months and F-event that a randomly selected adult American is female Assume that P(F) 0.5. Are the events L and F independent events? Use probabilities to justify your answer. Land Flare notindependent events, because P(L) P(F)- 0.3 , which is not equal to P(L n F)

## Related Questions

What is the circumference of circle p?

C = 2 pi r, and r = 3ft, so C=2*pi*3 = 6pi ft.

6π ft

Step-by-step explanation:

PA=3ft

I need help with this ^

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What is the y-intercept of function f?A. 1

B. -1

C. -2

D. 5

1

Step-by-step explanation:

The y intercept is when x =0

We need to use the second equation

-x+1  since -2 < 0 <3

0+1

The y intercept is 1

The distribution of the annual incomes of a group of middle management employees approximated a normal distribution with a mean of $37,200 and a standard deviation of$800. About 68% of the incomes lie between what two incomes

68% of the incomes lie between $36,400 and$38,000.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ =  $37,200 Standard Deviation, σ =$800

We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.

Empirical rule:

• Almost all the data lies within three standard deviation of mean for a normally distributed data.
• About 68% of data lies within one standard deviation of mean.
• About 95% of data lies within two standard deviation of mean.
• About 99.7% of data lies within three standard deviation of mean.

Thus, 68% of data lies within one standard deviation.

Thus, 68% of the incomes lie between $36,400 and$38,000.

Suppose 41%41% of American singers are Grammy award winners. If a random sample of size 860860 is selected, what is the probability that the proportion of Grammy award winners will differ from the singers proportion by less than 5%5%?

99.72% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 5%.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use the z-score formula.

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

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

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

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation

In this question:

So

What is the probability that the proportion of Grammy award winners will differ from the singers proportion by less than 5%?

This is the pvalue of Z when X = 0.41 + 0.05 = 0.46 subtracted by the pvalue of Z when X = 0.41 - 0.05 = 0.36. So

X = 0.46

By the Central Limit Theorem

has a pvalue of 0.9986

X = 0.36

has a pvalue of 0.0014

0.9986 - 0.0014 = 0.9972

99.72% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 5%.

What does the letter U stand for 25 > u-7