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Sveta_85 [38]
2 years ago
6

                                         Three friends are renting

Mathematics
1 answer:
nexus9112 [7]2 years ago
7 0

It is given that:

Monthly Rent = A

Total Money Paid to Landlord = Y

The landlord requires initial payment to include:

  • 1st month's rent
  • \frac{1}{2} month's rent or 50% of monthly rent for Security Deposit
  • 40% of monthly rent for  utility bills
  • 5% of monthly rent for health club
  • 13% of monthly rent per person for other services

Also, Total Amount Paid to the Landlord = $2574

Number of People Sharing the Apartment = 3

Basis the above information,

Y = (100% * A) + (50% * A) + (40% * A) + (5% * A) + (13% * A * 3)

⇒ Y = A + (0.5 * A) + (0.4 * A) + (0.05 * A) + (0.39 * A)

⇒ Y = A + (0.5 * A) + (0.4 * A) + (0.05 * A) + (0.39 * A)

⇒ Y = 2.34 * A

Substituting the value of Y to determine A

⇒ 2,574 = 2.34 * A

⇒ A = 1,100

Hence, the monthly rent is $1,100

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kupik [55]

Answer:

a) P(64.2

b) 69.764

Step-by-step explanation:

1) 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".

2) Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(65.5,2.6)

Where \mu=65.5 and \sigma=2.6

We are interested on this probability

P(64.2

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(64.2

And we can find this probability on this way:

P(-0.50

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

P(-0.50

3) Part b

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.05   (a)

P(X   (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 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=1.64

And if we solve for a we got

a=65.5 +1.64*2.6=69.764

So the value of height that separates the bottom 95% of data from the top 5% is 69.764.

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