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Natasha2012 [34]
3 years ago
13

The weekly earnings of students in one age group are normally distributed with a standard deviation of 47 dollars. A researcher

wishes to estimate the mean weekly earnings of students in this age group. Find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 5 dollars. 6 8 37 340
Mathematics
1 answer:
ELEN [110]3 years ago
7 0

Answer:

Option D) 340

Step-by-step explanation:

We are given the following in the question:

Alpha, α = 0.05

Population standard deviation, σ = $47

Margin of error = 5

95% Confidence Interval:

\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}

\text{Margin of error} = z_{critical}\frac{\sigma}{\sqrt{n}}

Putting the values, we get,

z_{critical}\text{ at}~\alpha_{0.05} = 1.96

5 = 1.96(\dfrac{47}{\sqrt{n}} )\\\\\sqrt{n} = \dfrac{47\times 1.96}{5}\\\\n = 339.443776\\\Rightarrow n \approx 340

Thus, the correct answer is

Option D) 340

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The sum of two numbers is 41. The larger number is one less than twice the smaller number. Find the numbers.
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Step-by-step explanation:

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Answer:

7th week

Step-by-step explanation:

Let us represent the number of weeks as x

Jill begins the summer with $500 in her savings account. Each week, she withdraws $20.

$500 - $20× x

500 - 20x

Her brother, Sam,starts the summer with $150 in his account. He adds $30 to his account each week.

$150 + $30 × x

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We solve this be Equating both Equations together

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