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grin007 [14]
3 years ago
12

Susan opened a college savings account 4 years ago. She opened the account with an initial deposit of $3,000. Starting the next

year, she deposited $1,000 on the same day each year. The account earns interest at an annual rate of 4.15% and is compounded annually. Susan hopes to have earned enough interest to pay for her first year of college tuition, which costs $7,100. What is the difference between her ending balance after 4 years and the cost of her tuition?
Mathematics
2 answers:
Oksi-84 [34.3K]3 years ago
6 0
What did you sayyyyyyyyyyy
alina1380 [7]3 years ago
5 0

Step-by-step explanation:

3.9 percent

gfdsryuvcnkijnvcddxxcccvhjurddcccz

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Refer to Exercise 3.122. If it takes approximately ten minutes to serve each customer, find the mean and variance of the total s
garri49 [273]

Answer

a. The expected total service time for customers = 70 minutes

b. The variance for the total service time = 700 minutes

c. It is not likely that the total service time will exceed 2.5 hours

Step-by-step explanation:

This question is incomplete. I will give the complete version below and proceed with my solution.

Refer to Exercise 3.122. If it takes approximately ten minutes to serve each customer, find the mean and variance of the total service time for customers arriving during a 1-hour period. (Assume that a sufficient number of servers are available so that no customer must wait for service.) Is it likely that the total service time will exceed 2.5 hours?

Reference

Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour.

From the information supplied, we denote that

X= Customers that arrive within the hour

and since X follows a Poisson distribution with mean \alpha = 7

Therefore,

E(X)= 7

& V(X)=7

Let Y = the total service time for customers arriving during the 1 hour period.

Now, since it takes approximately ten minutes to serve each customer,

Y=10X

For a random variable X and a constant c,

E(cX)=cE(X)\\V(cX)=c^2V(X)

Thus,

E(Y)=E(10X)=10E(X)=10*7=70\\V(Y)=V(10X)=100V(X)=100*7=700

Therefore the expected total service time for customers = 70 minutes

and the variance for serving time = 700 minutes

Also, the probability of the distribution Y is,

p_Y(y)=p_x(\frac{y}{10} )\frac{dx}{dy} =\frac{\alpha^{\frac{y}{10} } }{(\frac{y}{10})! }e^{-\alpha } \frac{1}{10}\\ =\frac{7^{\frac{y}{10} } }{(\frac{y}{10})! }e^{-7 } \frac{1}{10}

So the probability that the total service time exceeds 2.5 hrs or 150 minutes is,

P(Y>150)=\sum^{\infty}_{k=150} {p_Y} (k) =\sum^{\infty}_{k=150} \frac{7^{\frac{k}{10} }}{(\frac{k}{10})! }.e^{-7}  .\frac{1}{10}  \\=\frac{7^{\frac{150}{10} }}{(\frac{150}{10})! } .e^{-7}.\frac{1}{10} =0.002

0.002 is small enough, and the function \frac{7^{\frac{k}{10} }}{(\frac{k}{10} )!} .e^{-7}.\frac{1}{10}  gets even smaller when k increases. Hence the probability that the total service time exceeds 2.5 hours is not likely to happen.

3 0
2 years ago
benjamin is 4 years younger the kevan william is 4 years less than twice benjamins age if willian is 22 how old are kevan and be
meriva
Kevin would be 14 and Benjamin would be 10
7 0
2 years ago
Three divided by four
muminat

Answer:

0.75

Step-by-step explanation:

3/4=0.75

Hope this helps! :)

8 0
3 years ago
Given the function f(x) = 2x, find the value of f−1(32).
Oliga [24]

Answer:

it is -30

Step-by-step explanation:

you would divide both sides by x,then f=2

using PEMDAS we come to -30

5 0
3 years ago
ANY HELP IS APPRECIATED YALL! PLEASE HELP A GIRL OUT :D THANK YOU FOR TAKING YOUR TIME TO HELP ME:)
nignag [31]
D. 180/4=45. That’s the distance in an hour. Then multiply that by 8.
3 0
2 years ago
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