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find the indicated probability and interpret the result from 1975 through 2020 the mean annual gain of the dow jones indus

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Find the indicated probability and interpret the result. From 1975 through 2020, the mean annual gain of the Dow Jones Industrial Average was 651. A random sample of 35 years is selected from this population. What is the probability that the mean gain for the sample was between 400 and 700? Assume sigmaequals1540. Question content area bottom Part 1 The probability is enter your response here. (Round to four decimal places as needed.)

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Answer to a math question Find the indicated probability and interpret the result. From 1975 through 2020, the mean annual gain of the Dow Jones Industrial Average was 651. A random sample of 35 years is selected from this population. What is the probability that the mean gain for the sample was between 400 and 700? Assume sigmaequals1540. Question content area bottom Part 1 The probability is enter your response here. (Round to four decimal places as needed.)

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101 Answers

Given:
Population mean (

\mu

) = 651
Population standard deviation (

\sigma

) = 1540
Sample size (

n

) = 35

To find the probability that the mean gain for the sample was between 400 and 700, you need to first calculate the standard error of the mean:

SE = \frac{\sigma}{\sqrt{n}}

SE = \frac{1540}{\sqrt{35}} \approx 260.65

Next, calculate the Z-scores for both 400 and 700:

Z_{400}=\frac{400 - 651}{260.65}\approx-0.964

Z_{700}=\frac{700 - 651}{260.65}\approx0.188

Using a Z-table or calculator, find the probabilities corresponding to these Z-scores:

The answer is:

0.4029

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