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butalik [34]
2 years ago
5

April runs a small shop where she provides a service. She is able to process an average of 11 customers per hour. An average of

7 customers per hour seek this service at her shop. What is:
Business
1 answer:
professor190 [17]2 years ago
4 0

Answer:

5. Po= 0.36

6. Pn = 0.04

7. 0.16

8. 1.11

9. 1.75

10. 9.9

Explanation:

5. Computation for the probability that April will not be working with a customer

Using this formula

Po=1-(Average number of arrival per hour/Average number of customer served per hour)

Let plug in the formula

Po= 1-(7/11 )

Po=1-0.64

Po= 0.36

Therefore the probability that April will not be working with a customer will be 0.36

6. Calculation for the probability of 5 customers in the system

Using this formula

Pn= (Average number of arrival per hour/Average number of customer served per hour)* Po

Let plug in the formula

Pn= (7/11)^5* 0.36

Pn=0.104358*0.36

Pn=0.037

Pn = 0.04 (Approximately)

Therefore the probability of 5 customers in the system will be 0.04

7. Calculation for the average time a customer spends waiting in line

Time spend Waiting in line=7^2/11(11 – 7) /7

Time spend Waiting in line=(49/44)/7

Time spend Waiting in line = 1.11/7

Time spend Waiting in line= 0.16

Therefore the average time a customer spends waiting in line will be 0.16

8. Calculation for the average number of customers waiting in line

Customers waiting in line = 7^2/11(11 – 7)

Customers waiting in line=49/44

Customers waiting in line= 1.11

Therefore the average number of customers waiting in line will be 1.11

9. Calculation for the average number of customers in the system

Average customers in the system= 1.11 +(7/11)

Average customers in the system= 1.11 +0.64

Average customers in the system = 1.75

Therefore the average number of customers in the system will be 1.75

10. Calculation for the arrival rate in order for April to stay that busy

Arrival rate = 0.9 * 11

Arrival rate = 9.9

Therefore the arrival rate in order for April to stay that busy will be 9.9

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2 years ago
RuthAnn is 28 years old and is retiring at the age of 65. When she retires, she estimates that she will need an annual income of
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Answer:

Yes

Explanation:

From her current age of 28 to her retirement age of 65, RuthAnn has (65 - 28 =) 37 more years to work.

If she saves 11% of her annual income of $36,278.13 into a 401(k), she will be setting aside (11% * 36,278.13 =) $3,990.59 into the 401(k) account annually.

At 7.1% compounding rate, in 37 years, RuthAnn would have set aside an amount estimated by the future value of an annuity formula.

FV = \frac{A(1+r)^{n} - 1}{r}

where FV is the future value, the amount that would have been set aside,

A = is the annual savings,

r = is the compounding rate, and

n = is the number of years.

Therefore, the total amount that would be saved up after 37 years =

FV = \frac{3,990.59(1+0.071)^{37} - 1}{0.071}

= (3,990.59 * 11.6535)/0.071

= $654,990.31.

By spending $32,523 annually from an account earning 7.1% compound interest rate for 30 years, the present value of the total amount needed by RuthAnn today that will be sufficient for her retirement spending can be estimated using the present value of an annuity formula.

PV = \frac{A(1 - (1+r)^{-n}}{r}

= PV = \frac{32,523(1 - (1.071)^{-30}}{0.071}

= (32523 * 0.8723)/0.071

= $399,574.83.

Since the amount saved up ($654,990.31) is more than the total amount required for RuthAnn's retirement ($399,574.83), RuthAnn has more than sufficient to meet her Retirement goal.

Specifically, the amount she has saved up can support a maximum annual spending which can be estimated from the present value of an annuity formula.

PV = \frac{A(1 - (1+r)^{-n}}{r}

where PV = the amount saved up, $654,990.31,

A = the annual spending which we are estimating,

r = the 7.1% compound interest rate,

n = the number of years to retirement.

654,990.31 = \frac{A(1 - (1.071)^{-30}}{0.071}

= 654,990.31 = (A * 0.8723)/0.071

= A = 654,990.31/0.8723 * 0.071

= A = 53,312.29

Thus, the amount saved up can support a maximum retirement spending of $53,312.29, which is higher than the $32,523 annual income needed by RuthAnn for her retirement.

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