Alan is connecting three garden hoses to make one longer hose.The green hose is 6.25 feel long the orange hose is 5.755 feet lon
1 answer:
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Answer:
(a) <em> </em><em>n</em> : 20 50 100 500
P (-200 < <em>X</em> - <em>μ </em>< 200) : 0.2886 0.4444 0.5954 0.9376
(b) The correct option is (b).
Step-by-step explanation:
Let the random variable <em>X</em> represent the amount of deductions for taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return.
The mean amount of deductions is, <em>μ</em> = $16,642 and standard deviation is, <em>σ</em> = $2,400.
Assuming that the random variable <em>X </em>follows a normal distribution.
(a)
Compute the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean as follows:
- For a sample size of <em>n</em> = 20
- For a sample size of <em>n</em> = 50
- For a sample size of <em>n</em> = 100
- For a sample size of <em>n</em> = 500
<em> n</em> : 20 50 100 500
P (-200 < <em>X</em> - <em>μ </em>< 200) : 0.2886 0.4444 0.5954 0.9376
(b)
The law of large numbers, in probability concept, states that as we increase the sample size, the mean of the sample () approaches the whole population mean (
).
Consider the probabilities computed in part (a).
As the sample size increases from 20 to 500 the probability that the sample mean is within $200 of the population mean gets closer to 1.
So, a larger sample increases the probability that the sample mean will be within a specified distance of the population mean.
Thus, the correct option is (b).
Answer:
<em>The table shows an exponential function</em>
Step-by-step explanation:
<u>Linear vs Exponential Functions</u>
A linear function is written as:
where m and b are constants.
If a table contains a linear function, then for each pair of ordered pairs (x1,y1) and (x2,y2), the value of m must be constant.
The slope can be calculated as:
An exponential function is written as:
Where r is the ratio and yo is a constant.
If a table contains an exponential function, for two ordered pairs (x1,y1) and (x2,y2), the value of r must be constant.
The ratio can be calculated as:
Calculate the slope for (0,4) and (1,2):
Calculate the slope for (1,2) and (2,1):
Since the slope is not the same, the function is not linear.
Now calculate the ratio for (0,4) and (1,2)
The radical of index 1 is simply equal to its argument:
Now calculate the ratio for (0,4) and (2,1)
Testing other points we'll find the same ratio, thus the table is an exponential function