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3 years ago

In this scatterplot, the horizontal axis indicates years

Mathematics

1 answer:

jonny [76]3 years ago

8 0

Answer:

Population of wolves in 2016 = 23

Step-by-step explanation:

Equation of the line of best fit has been given as,

y = 1.5x - 1

Here, y = population of a pack of wolves

x = duration (in years) since year 2000

Duration between year 2000 and 2016 = 16 years

Now we substitute the value x = 16 in the equation of line of best fit,

y = 1.5(16) - 1

y = 24 - 1

y = 23

Therefore, population of wolves in 2016 = 23

You might be interested in

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as t

skad [1K]

Answer:

a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.

This means that $\mu = 273, \sigma = 100$

A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?

Sample of 30 means that $n = 30, s = \frac{100}{\sqrt{30}}$

The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So

X = 289

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

By the Central Limit Theorem

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

$Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}$

$Z = 0.88$

$Z = 0.88$ has a p-value of 0.8106

X = 257

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

$Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}$

$Z = -0.88$

$Z = -0.88$ has a p-value of 0.1894

0.8106 - 0.1894 = 0.6212

0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.

B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?

Sample of 30 means that $n = 50, s = \frac{100}{\sqrt{50}}$

X = 289

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

By the Central Limit Theorem

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

$Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}$

$Z = 1.13$

$Z = 1.13$ has a p-value of 0.8708

X = 257

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

$Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}$

$Z = -1.13$

$Z = -1.13$ has a p-value of 0.1292

0.8708 - 0.1292 = 0.7416

0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.

C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?

Sample of 30 means that $n = 100, s = \frac{100}{\sqrt{100}}$

X = 289

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

By the Central Limit Theorem

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

$Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}$

$Z = 1.6$

$Z = 1.6$ has a p-value of 0.9452

X = 257

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

$Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}$

$Z = -1.6$

$Z = -1.6$ has a p-value of 0.0648

0.9452 - 0.0648 =

0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.

D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?

None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.

6 0

3 years ago

Erin is buying a tv with an original price of 650. She receives a 20% discount. How much will Erin pay, before tax, for the TV

r-ruslan [8.4K]

Answer:

$520

Step-by-step explanation:

20%

=0.2

0.2*650

=130

650-130

=520

5 0

3 years ago

HELP BECAUSE IM STUPID!

mixer [17]

I don't think you're stupid. ^^
Let's take the third term, 8. If n=3, then an should be 8.
The first answer gives 15+2.5*3=22.5.
The second answer gives 15.5+2.5=23.
The third answer gives 15-2.5*3=7.5.
The fourth answer gives 15.5-2.5*3=8.
Choice 4 is correct.

Let's try to actually find the equation on our own.
The equation for an arithmetic series is an=a0+dn where a0 is the term that comes before the first term.
The first term given is 13 and it decreases by 2.5 each time so n=-2.5 and the term that would be before 13 is 15.5.
Thus the equation is an=15.5-2.5n

6 0

3 years ago

Read 2 more answers

A coffee franchise is opening a new store. The company estimates that there is a 70% chance the store will have a profit of $50,

aivan3 [116]

Step-by-step explanation:

The expected value is the sum of each outcome times its probability.

E = (0.70)(50000) + (0.05)(0) + (0.25)(-3500)

E = 34125

The store is expected to gain $34,125.

8 0

3 years ago

72 ounces in 6 steaks

Alona [7]

The unit rate is the total ounces divided by the total number of steaks:

72 ounces / 6 steaks = 12 ounces per steak.

3 0

3 years ago