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borishaifa [10]

3 years ago

14

A sinking fund is being established the goal of which is to reach $100,000. Calculate the payment where i is the interest rate p

er period. N= 22 i= .03

1 answer:

Vika [28.1K]3 years ago

5 0

Answer:

<u>Initial deposit = $ 60,241 (Rounding to the next whole dollar)</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Future Value = 100,000

Interest rate = 0.03

N = 22

2. Let's calculate the initial deposit for the sinking fund, this way:

Future Value = Initial deposit * (1 + i*N)

Replacing with the real values:

100,000 = Initial deposit * (1 + 0.03 * 22)

100,000 = 1.66 Initial deposit

Initial deposit = 100,000/1.66

<u>Initial deposit = $ 60,241 (Rounding to the next whole dollar)</u>

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Assume that females have pulse rates that are normally distributed with a mean of μ=73.0 beats per minute and a standard deviati

Gennadij [26K]

Answer:

a. the probability that her pulse rate is less than 76 beats per minute is 0.5948

b. If 25 adult females are randomly selected, the probability that they have pulse rates with a mean less than 76 beats per minute is 0.8849

c. D. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

Step-by-step explanation:

Given that:

Mean μ =73.0

Standard deviation σ =12.5

a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 76 beats per minute.

Let X represent the random variable that is normally distributed with a mean of 73.0 beats per minute and a standard deviation of 12.5 beats per minute.

Then : X $\sim$ N ( μ = 73.0 , σ = 12.5)

The probability that her pulse rate is less than 76 beats per minute can be computed as:

$P(X < 76) = P(\dfrac{X-\mu}{\sigma}< \dfrac{X-\mu}{\sigma})$

$P(X < 76) = P(\dfrac{76-\mu}{\sigma}< \dfrac{76-73}{12.5})$

$P(X < 76) = P(Z< \dfrac{3}{12.5})$

$P(X < 76) = P(Z< 0.24)$

From the standard normal distribution tables,

$P(X < 76) = 0.5948$

Therefore , the probability that her pulse rate is less than 76 beats per minute is 0.5948

b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.

now; we have a sample size n = 25

The probability can now be calculated as follows:

$P(\overline X < 76) = P(\dfrac{\overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{ \overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}})$

$P( \overline X < 76) = P(\dfrac{76-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{76-73}{\dfrac{12.5}{\sqrt{25}}})$

$P( \overline X < 76) = P(Z< \dfrac{3}{\dfrac{12.5}{5}})$

$P( \overline X < 76) = P(Z< 1.2)$

From the standard normal distribution tables,

$P(\overline X < 76) = 0.8849$

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

In order to determine the probability in part (b); the normal distribution is perfect to be used here even when the sample size does not exceed 30.

Therefore option D is correct.

Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

5 0

2 years ago

Tom wants to buy some protein bars and magazines for a trip he has decided to buy three times as many protein bars with magazine

kumpel [21]

Answer:12 Protein bar and 3 magazines

Step-by-step explanation:

Given

Tom purchases Protein bars 3 times as much as magazine

Each bar cost $\$ 0.7$

Each magazine costs $\$ 2.50$

Sales tax is 6.5 %

suppose Tom buy x magazines so

Price of magazine is $2.5 x$

Price of bars is $3\times 0.7x=2.1 x$

Total Price $=2.5 x+2.1 x=4.6 x$

After sales tax $=4.6x(1+0.065)=4.899 x$

This must be less than $\$ 20$

so $4.899x < 20$

$x< 4.082$

thus $x=4$

so he but 4 magazines and 12 protein bars

3 0

3 years ago

what is the value of the x variable in the solution to the following system of equations? 2x 2y = 6 x 3y = −1 a. −2 b. 2 c. 5 d.

tatuchka [14]

2x + 2y = 6 . . . . . (1)
x + 3y = -1 . . . . . (2)

(1) x 3 => 6x + 6y = 18 . . . . . (3)
(2) x 2 => 2x + 6y = -2 . . . . . (4)

(3) - (4) => 4x = 20
x = 20/4 = 5

7 0

3 years ago

A biased dice was rolled and the scores recorded in the table below

dusya [7]

Given:

The table of score and frequency.

To find:

The probability that on the next roll the score will be 4.

Solution:

From the given table it is clear that the score 4 occurs 10 times.

Number of times the dice was rolled = 17 + 24 + 23 + 10 + 16 + 30

= 120

The probability that on the next roll the score will be 4 is

$\text{Required probability}=\dfrac{\text{Number of times 4 occurs}}{\text{Number of times the dice was rolled}}$

$\text{Required probability}=\dfrac{10}{120}$

$\text{Required probability}=\dfrac{1}{12}$

Therefore, the required probability is $\dfrac{1}{12}$ .

8 0

3 years ago

Which set is in order from smallest to largest?

shutvik [7]

D. will be your answer.

7 0

3 years ago