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oksian1 [2.3K]
2 years ago
8

How do I solve

bsmiddle" class="latex-formula">?
I think the answer is 1 (I could be wrong) but I can't figure out the steps and the work to get the correct answer. Would appreciate some help :)
Mathematics
1 answer:
olga2289 [7]2 years ago
6 0

Answer:

Yes, buddy ut's 1 your correct x

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The mean per capita income is 16,127 dollars per annum with a variance of 682,276. What is the probability that the sample mean
MakcuM [25]

Answer:

0.60% probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected

Step-by-step explanation:

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

Normal probability distribution:

Problems of normally distributed samples are solved using 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 random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation, which is also called standard error s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

The standard deviation is the square root of the variance. So

\mu = 16127, \sigma = \sqrt{682276} = 826, n = 476, s = \frac{826}{\sqrt{476}} = 37.86

What is the probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected

Either it differs by 104 or less dollars, or it differs by more than 104 dollars. The sum of the probabilities of these events is 100. I am going to find the probability that it differs by 104 or less dollars first.

Probability that it differs by 104 or less dollars first.

pvalue of Z when X = 16127 + 104 = 16231 subtracted by the pvalue of Z when X = 16127 - 104 = 16023. So

X = 16231

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

By the Central Limit Theorem

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

Z = \frac{16231 - 16127}{37.86}

Z = 2.75

Z = 2.75 has a pvalue of 0.9970

X = 16023

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

Z = \frac{16023 - 16127}{37.86}

Z = -2.75

Z = -2.75 has a pvalue of 0.0030

0.9970 - 0.0030 = 0.9940

99.40% probability that it differs by 104 or less.

What is the probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected

p + 99.40 = 100

p = 0.60

0.60% probability that the sample mean would differ from the true mean by more than 104 dollars if a sample of 476 persons is randomly selected

7 0
3 years ago
Can u solve this for me: 72 + 4x = 2x + 82 and please show work
8_murik_8 [283]
The answer is X = 5 because first you have to take away 2x from that side so u minus 2x from 4x that gives u: 72 + 2x = 82 then you have to minus 72 from both sides and that gives you 2x = 10 once you have that you divide both sides by 2 because you want the X by itself and once you get that X = 5. Hope this helped!
8 0
3 years ago
Read 2 more answers
The image is below please help I am crying
Veronika [31]

Answer:

Quadrant III

Step-by-step explanation:

7 0
2 years ago
HELP ME QUICK PLEASEE!!
Lena [83]

Answer:

  A) is a function

  B) f(x) is greater

  C) x = 12

Step-by-step explanation:

A) Yes, the relation is a function.

A function has a unique input value for each output value. There are no repeated x-values, so this relation is a function.

__

B) The table says y=6 for x=6.

  f(6) = 2(6)+16 = 28

f(x) has a greater value for x=6.

__

C) Substituting the given information, we have ...

  40 = 2x +16

  24 = 2x

  12 = x

The value of x is 12 when f(x) is 40.

3 0
3 years ago
Robbert wants to put lights around the edge of his yard.The yard if 40 feet long and 23 feet wide.How many yards of light does h
slega [8]

Answer:

102.222 square yards of light.

Step-by-step explanation:

From the above question, the yard had the dimensions 40 feet long and 23 feet wide.

Hence, the yard is rectangular in shape.

We have to find the area of the yard.

The formula is given as:

Area = Length × Width

= 40 feet × 23 feet

= 920 square feet

Converting to yards

1 square foot = 0.111 square yard

920 square feet = x

Cross Multiply

x = 920 × 0.111 square yard

x = 102.222 square yards.

Therefore, Robbert would need 102.222 square yards of light.

6 0
3 years ago
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