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rjkz [21]
2 years ago
15

What single percentage change is equivalent to a 11% increase followed by a 15% increase?​

Mathematics
1 answer:
AlekseyPX2 years ago
7 0

Answer:

It's a total increase by 27,65%

Step-by-step explanation:

1,11 × 1,15 = 1,2765

1,2765 = +27,65%

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A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimat
zmey [24]

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

In this question, we have that:

\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

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

X = 205

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

Z = \frac{205 - 200}{5}

Z = 1

Z = 1 has a pvalue of 0.8413.

X = 195

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

Z = \frac{195 - 200}{5}

Z = -1

Z = -1 has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

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

Z = \frac{210 - 200}{5}

Z = 2

Z = 2 has a pvalue of 0.9772.

X = 195

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

Z = \frac{190 - 200}{5}

Z = -2

Z = -2 has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

7 0
3 years ago
When testing a claim that the mean head circumference for newborn American infants is greater than 35.8 centimeters a random sam
Mila [183]

Answer:

hi

Step-by-step explanation: first you type h then you type i then it makes hi

8 0
2 years ago
Simplify (square root 2)( square root of 2^3)
steposvetlana [31]

Answer:

\large\boxed{(\sqrt2)(\sqrt{2^3})=4}

Step-by-step explanation:

(\sqrt2)(\sqrt{2^3})\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{2\cdot2^3}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\sqrt{2^{1+3}}=\sqrt{2^4}\\\\(1)=\sqrt{2^{2\cdot2}}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt{(2^2)^2}\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=2^2=4\\\\(2)=\sqrt{2\cdot2\cdot2\cdot2}=\sqrt{16}=6\ \text{because}\ 4^2=16

8 0
3 years ago
Solve for x. please show work
Mazyrski [523]
Those 2 angles makes up corresponding angles in parallel lines. Which means, both two angles equal to each other because this is a rule that exists when both of the lines are parallel to each other which is indicated with red arrows in the photo.
75 = 11x - 2
75 + 2 = 11x
77 = 11x
X = 77 / 11
X = 7
The answer is 7.
3 0
3 years ago
At Best Buy they have a stereo system that sells for $2500 and is on sale for 9% and sales tax is 5%. What is the final cost?
Vedmedyk [2.9K]

Answer:

Final cost = $2388.75

Step-by-step explanation:

Cost of stereo system = $2500

Sale = 9%

Cost of sale = 9% of 2500

Cost of sale = \frac{9}{100}*2500 = 0.09*2500

Cost of sale = $225

Price after sale = 2500 - 225 = $2275

Sales tax = 5% of 2275

Sales tax = 0.05 * 2275 = $ 113.75

Final cost = 2275 + 113.75 = $2388.75

7 0
3 years ago
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