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Ilia_Sergeevich [38]
3 years ago
8

You are going on a field trip in a school bus. A special detector placed on one of the bus's tires counts the number of rotation

s completed by the tire during the journey. The tire's diameter is 111 meter, and it made 800080008000 rotations during the trip.
How far did the bus travel?
Mathematics
1 answer:
KIM [24]3 years ago
5 0

First you need to find the circumference of the circle because 1 revolution is 1 length of the circumference. The formula for the circumference is C=2πr or C=πd, if the diameter is 1 meter then the circumference is π1 which is just π, and if it travelled 8000 rotations then that would mean it travelled 8000π, so it travelled 8000π in meters

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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
Plz help i will mark u brainlyest.
spin [16.1K]
A = 5, -10
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Dovator [93]

Answer:

For the first one ASA

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Step-by-step explanation:

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Name three radii of Circle S.
Talja [164]

Answer:

circle S radii SU, ST, SR

Circle U radii UT, US, UR

Step-by-step explanation:

Radii start in the middle of the circle to the end of the circle.

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Solve for the x in the diagram below. 50°, 2x°, and 150°
lapo4ka [179]

Answer:

50 degrees.

Step-by-step explanation:

The angle where 2x + 50 is congruent to the 150 degree angle because they are vertical angles.

2x + 50 = 150

2x = 100

x = 50.

Hope this helps!

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3 years ago
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