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lawyer [7]
3 years ago
12

jacob bought 5 pencils for 80 cents. At this same rate, how many pencils can hee but for 40 cents? Explain why this answer does

not make sense
Mathematics
1 answer:
Step2247 [10]3 years ago
3 0
5 pencils cost $.80. Each pencil costs $0.16
Then divide $0.16 into $0.40
This equals 2.5 pencils, you can't buy half a pencil
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
2 years ago
1. Classify each statement as true or false for all real numbers a, b,<br> and c.
12345 [234]

naw

g4jtnbjtrnjbnrtibnrijnbngtrjnb jtkgnbrbgbn

6 0
2 years ago
A car used 5 2/3 gallons of fuel on a 3 hour trip. How many gallons were used each hour?
mr_godi [17]

Answer:

2. 1 8/9 gallons

Step-by-step explanation:

5 2/3 divided by 3

5.66666667/3 = 1.88888889

.88888889 = 8/9

1 + 8/9 = 1 8/9

5 0
2 years ago
How would you graph f(x) = 7x + 5 when you reflect it over y axis and translate it 3 units left
SOVA2 [1]

Answer:

See explanation

Step-by-step explanation:

Given the function f(x)=7x+5

1. To reflect the graph of the function f(x) over the y-axis, you should change the slope of the line in opposite. The slope of the function f(x) is 7, so the slope of the reflected function will be -7 and the expression of the reflected function will be

g(x)=-7x+5

2. To translate the function g(x) 3 units left, add 3 units to x, thus the expression for the function will be

h(x)=-7(x+3)+5\\ \\h(x)=-7x-21+5\\ \\h(x)=-7x-16

See attached diagram for details.

8 0
3 years ago
How to solve the area of a triangle
drek231 [11]
<h2>The area A of a triangle is given by the formula A=1/2*b*h where b is the base and h is the height of the triangle.</h2>

Step-by-step explanation:

<h2>The photo which is in the attachment is an example for your question. </h2>

<h2>hope this answer helps you!!</h2>

7 0
3 years ago
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