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harina [27]
3 years ago
9

Convert to a fraction 12 3\100​

Mathematics
1 answer:
sashaice [31]3 years ago
8 0

Answer:

1203/100

Step-by-step explanation:

12 times 100 equals 1200 plus three equals 1203/100

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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
What is the equation of the line that passes through the point (1,7) and is perpendicular to the graph of Y=-14X+11
vlada-n [284]
Y=1/14x might be the answer
4 0
3 years ago
HELP!! 100 POINTS!!
NNADVOKAT [17]

Answer:

x=9 x=-1

Step-by-step explanation:

x²-8x-9=0    a=1 b=-8 c=-9

you have to use the quadratic formula to get the values.

5 0
3 years ago
Read 2 more answers
Why the output is a zero number ?<br><img src="https://tex.z-dn.net/?f=%28x%20-%203%29%20%5Ctimes%20%28x%20%20%20%2B%204%29%20%3
ELEN [110]

Answer:

see explanation

Step-by-step explanation:

Given

(x - 3) × (x + 4) = 0, that is

(x - 3)(x + 4) = 0

The zero product indicates that (x - 3) = 0 or (x + 4) = 0

x - 3 = 0 ⇒ x = 3

x + 4 = 0 ⇒ x = - 4

Thus if x = 3, then

(3 - 3)(x + 4) = 0 × (x + 4) = 0

Similarly if x = - 4 the output is zero

4 0
3 years ago
Assign two variables for each problem, and write the equations. Do not solve.
NemiM [27]
Price of boots is represented as x, price of tennis shoes is represented as y. x-y=44.38 x+y=196.12 Isolate x. (Or y, if you wanted to) x=y+44.38 x=196.12-y Set them equal to each other. y+44.38=196.12-y Solve for y. Then plug it in to either of the two original equations to find x. x=120.24 y=75.86 Note: This is assuming that the boots are more expensive than the tennis shoes. If the tennis shoes are more expensive than the boots, then the prices would be switched. I didn't find this clear in your question.
6 0
3 years ago
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