The variable y varies directly with the variable x.
1 answer:
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Amount spent for food = $5850, housing = $4680, clothing = $2340, savings = $2600, taxes = $5850, expenses = $2080.
<u>Step-by-step explanation:</u>
Step 1:
Given details are Total Income = $23,400
Step 2:
Amount spent for food, F= 1/4th of 23,400 =
= $5850
Step 3:
Amount spent for housing, H = 1/5th of 23,400 =
= $4680
Step 4:
Amount spent for clothing, C = 1/10th of 23,400 = = $2340
Step 5:
Amount spent for savings, S = 1/9th of 13,400 = = $2600
Step 6:
Amount spent for taxes, T = 1/4th of 23,400 = =$5850
Step 7:
Find amount spent on other expenses by totaling all expenditures and subtracting from the annual income.
Annual Income = F + H + C + S + T + E
Amount spent on other expenses, E = 23400 - (5850 + 4680 + 2340 + 2600 + 5850)
E = 23400 - 21320
E = $2080
Answer:
a)
b)
c)
And if we solve for a we got
So the value of height that separates the bottom 20% of data from the top 80% is 415.8.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
Let X the random variable that represent the SAT scores of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the complement rule and with the normal standard table or excel:
Part b
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with this difference:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
Part c
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.2 of the area on the left and 0.8 of the area on the right it's z=-0.842. On this case P(Z<-0.842)=0.2 and P(Z>-0.842)=0.8
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 20% of data from the top 80% is 415.8.