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Rama09 [41]
4 years ago
5

Simplify: 2{10-5+x[1+3(6-2)]}

Mathematics
1 answer:
REY [17]4 years ago
3 0

Answer:

10+26x

Step-by-step explanation:

To solve this, work your way from the inner most parentheses to the outer most:

  1. The inner most parentheses is around 6-2, meaning you solve this first. When you solve this, you get 4.
  2. The second most inner parentheses is around (1+3 times 4) using PEMDAS, you first solve the multiplication, and then add. Once you solve this, you get 13.
  3. Next, the outer most parentheses is around (10-5+13x). When you simplify this, you get 5+13x
  4. Finally, you multiply 2(5+13x). Using distributive property, you get 10+26x as your final simplified answer.
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Suppose that a random sample of size 36 is to be selected from a population with mean 50 and standard deviation 7. What is the a
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Answer:

The probability that the sample mean will be within 0.5 of the population mean is 0.3328.

Step-by-step explanation:

It is provided that a random variable <em>X</em> has mean, <em>μ</em> = 50 and<em> </em>standard deviation, <em>σ</em> = 7.

A  random sample of size, <em>n</em> = 36 is selected.

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

\mu_{\bar x}=\mu=50

And the standard deviation of the distribution of sample mean is given by,

\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{7}{\sqrt{36}}=1.167

So, the distribution of the sample mean of <em>X</em> is N (50, 1.167²).

Compute the probability that the sample mean will be within 0.5 of the population mean as follows:

P(|\bar X-\mu_{\bar x}|\leq 0.50)=P(-0.50

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Thus, the probability that the sample mean will be within 0.5 of the population mean is 0.3328.

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