Find the area of the figure. PLS I NEED HELP FAST!

Let the random variable X 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, μ = $16,642 and standard deviation is, σ = $2,400.

Assuming that the random variable X 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 n = 20

$P(\mu-200$

$=P(-0.37$

For a sample size of n = 50

$P(\mu-200$

$=P(-0.59$

For a sample size of n = 100

$P(\mu-200$

$=P(-0.83$

For a sample size of n = 500

$P(\mu-200$

$=P(-1.86$

n : 20 50 100 500

P (-200 < X - μ < 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 ( $\bar x$ ) approaches the whole population mean ( $\mu_{x}$ ).

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).

8 0

3 years ago

Sandra sells necklaces at a school craft fair. She uses the equation P= 7.5n - (2.25n + 15) to determine her total profit at th

gregori [183]

The way you find profit is to subtract the revenue and the cost
Profit = Revenue - Cost
The revenue is the amount of money coming in, the cost is the amount of money going out. The goal of course is to have the revenue larger than the cost so that the profit is positive.

So the equation given is
P = 7.5n - (2.25n+15)
and its in the form
P = R - C
where...
R = 7.5n is the revenue equation
C = 2.25n+15 is the cost equation

Focus on the revenue equation
R = 7.5n
which is the same as
R = 7.50*n

This tells us that Sandra pulls in a total of 7.50*n dollars where n is some positive whole number. It represents the number of necklaces sold. For example, if she sold n = 10 necklaces, then
R = 7.50*n
R = 7.50*10
R = 750
meaning that Sandra has made $750 in revenue

As you can see above, the revenue is computed by multiplying the price per necklace ($7.50) by the number of necklaces sold (n) to get R = 7.50*n

So that's why the answer is $7.50

Note: The 2.25 is part of the cost equation. This is known as the variable cost. It is the cost to make one necklace ignoring the fixed cost (eg: rent). The variable cost often doesn't stay the same, but algebra textbooks often simplify this aspect.

8 0

3 years ago

I usually have an answer to the question

Andru [333]

Answer:is this the question?

Step-by-step explanation:

7 0

2 years ago