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2 years ago

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James knows that he eventually wants to buy a motorcycle, and the model he has in mind costs $5,000. He has found a bank that wi

ll let him open a saving account with 7% interest that is compounded monthly. If he wants to buy his motorcycle in 5 years (he's still nervous), how much money should he invest in the account now

1 answer:

svetlana [45]2 years ago

4 0

Answer:

3527

Step-by-step explanation:

Using our compound interest formula we can plug in all of our given values and solve for P.

A(t)=P(1+r/n)^nt

5,000=P(1+0.07/12)^12(5)

P=5000/(1+0.07/12)^60

P≈$3,527

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Rocky Mountain National Park is a popular park for outdoor recreation activities in Colorado. According to U.S. National Park Se

Ugo [173]

Answer:

a) 0.6628 = 66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance

b) 0.5141 = 51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

c) 0.5596 = 55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

d) 0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 175$

(a) What is the probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance?

46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows. This means that $p = 0.467$ . So

$\mu = E(X) = np = 175*0.467 = 81.725$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.467*0.533} = 6.6$

This probability, using continuity correction, is $P(X \geq 85 - 0.5) = P(X \geq 84.5)$ , which is 1 subtracted by the pvalue of Z when X = 84.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{84.5 - 81.725}{6.6}$

$Z = 0.42$

$Z = 0.42$ has a pvalue of 0.6628.

66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance.

(b) What is the probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance?

Using continuity correction, this is $P(80 - 0.5 \leq X < 90 - 0.5) = P(79.5 \leq X \leq 89.5)$ , which is the pvalue of Z when X = 89.5 subtracted by the pvalue of Z when X = 79.5. So

X = 89.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{89.5 - 81.725}{6.6}$

$Z = 1.18$

$Z = 1.18$ has a pvalue of 0.8810.

X = 79.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{79.5 - 81.725}{6.6}$

$Z = -0.34$

$Z = -0.34$ has a pvalue of 0.3669.

0.8810 - 0.3669 = 0.5141

51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

(c) What is the probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance?

6.3% of visitors entered through the Grand Lake park entrance, which means that $p = 0.063$

$\mu = E(X) = np = 175*0.063 = 11.025$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.063*0.937} = 3.2141$

This probability, using continuity correction, is $P(X < 12 - 0.5) = P(X < 11.5)$ , which is the pvalue of Z when X = 11.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{11.5 - 11.025}{3.2141}$

$Z = 0.15$

$Z = 0.15$ has a pvalue of 0.5596.

55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

(d) What is the probability that more than 55 visitors have no recorded point of entry?

22.7% of visitors had no recorded point of entry to the park. This means that $p = 0.227$

$\mu = E(X) = np = 175*0.227 = 39.725$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.227*0.773} = 5.54$

Using continuity correction, this probability is $P(X \leq 55 + 0.5) = P(X \leq 55.5)$ , which is the pvalue of Z when X = 55.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{55.5 - 39.725}{5.54}$

$Z = 2.85$

$Z = 2.85$ has a pvalue of 0.9978

0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

8 0

2 years ago

Choose the situation that represents a function. The number of raisins in an oatmeal raisin cookie is a function of the diameter

expeople1 [14]

Answer: The time is takes to cook a turkey is a function of the turkey's weight.

In a function, there is an input and there is an output. The idea of a function is that each individual input is changed into an output.

The time it takes to cook a turkey depends on the size of the turkey.
Smaller turkeys would take less time to cook and larger turkeys would take longer to cook.

So if you start with the turkeys weight, you could determine how long it would need to cook. This is an example of a function.

5 0

2 years ago

Read 2 more answers

Total employment for sheet metal workers in 2016 is projected to be 201,000. if this is a 6.3% increase from 2006, approximately

fomenos

Answer:

Option d.

Step-by-step explanation:

Total employment for sheet metal workers in 2016 is projected to be = 201,000

This is a 6.3% increase from 2006.

Let the number of workers in 2006 be n

n + (6.3% of n) = 201,000

n + ( 0.063n) = 201,000

1.063n = 201,000

n = $\frac{201,000}{1.063}$

n = 189,087. 4882 ≈ 189,000

the total employment in 2006 was approximately 189,000

Option d is the answer.

8 0

2 years ago

Drag each situation to show whether it can be modeled using a linear or an exponential function. If the situation cannot be mode

lawyer [7]

Answer:

Step-by-step explanation:

A). An investment account earns 2.8% simple interest.

Since investment amount increases every year linearly, therefore, the modeled situation represents a LINEAR FUNCTION.

B). The price of a stock varies by 2.8% each week.

Since price of the stock may increase or decrease every week, therefore, this situation can't be modeled by any function.

Therefore, the answer is NEITHER.

C). An investment account earns 2.8% compound interest, compounded monthly.

Formula to get the value of the final amount in the account is,

Final value = Initial value × $(1+\frac{.028}{100})^t$

Here 't' = Duration of investment

It's an EXPONENTIAL FUNCTION.

3 0

2 years ago

Myra asked Annabelle to buy her some perfume while she was in France. Annabelle paid 200 euros for it. Myra wants to pay Annabel

serious [3.7K]

Answer:

286

Step-by-step explanation:

Given : Myra asked Annabelle to buy her some perfume while she was in France. Annabelle paid 200 euros for it. Myra wants to pay Annabelle back in U.S. dollars.

To Find: If the foreign exchange rate between the U.S. dollar and the euro is 1:0.7, how much should Myra pay Annabelle?

Solution:

Since Annabelle paid 200 euros

And Myra wants to pay Annabelle back in U.S. dollars.

Let Myra paid amount to Annabelle in U.S. dollar be x

We are also given that the U.S. dollar and the euro is 1:0.7

⇒ $\frac{1}{0.7}=\frac{x}{200}$

⇒ $\frac{1*200}{0.7}=x$

⇒ $\frac{200}{0.7}=x$

⇒ $285.7=x$

⇒285.7≈286

Thus Myra should pay $286 to Annabelle

6 0

2 years ago