A new game system was priced at $500 when it was introduced to the market. Over the
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).
Ow... this geometry is sure hard!!
.
Wait a second. Nope.
.
TWO SIDES!!
.
ITT!!
.
CONVERSE ITT!!
.
Converse Isosceles Triangle Theorem!
.
Look at the picture I attached.
.
Two angles equal... THE SIDES ADJACENT TO IT EQUAL!!
.
PERFECTO!!
.
Hope I helped!!
Source: I am learning Honors Geometry, near end of course.
.
Wait a second. Nope.
.
TWO SIDES!!
.
ITT!!
.
CONVERSE ITT!!
.
Converse Isosceles Triangle Theorem!
.
Look at the picture I attached.
.
Two angles equal... THE SIDES ADJACENT TO IT EQUAL!!
.
PERFECTO!!
.
Hope I helped!!
Source: I am learning Honors Geometry, near end of course.