Simplify 6t+t ????????

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

1.

Afina-wow [57]

Can you give us a photo

3 0

3 years ago

What is the slope of this line?

Bogdan [553]

Answer:

Slope = 6

Step-by-step explanation:

Reading your description carefully, the equation of line has been given to be

When we compare this with the standard form of a straight line

We immediately see that the slope or gradient m = 6.

Alternatively, when we consider the coordinates of the points mentioned, we have

(1, 5) ; (0, -1) ; (-1, -7)

We can take any two points out of these three and calculate the slope using the formula

For example, let us consider the points (1, 5) and (-1, -7)

Here x₁ = 1; x₂ = -1 and y₁ = 5; y₂ = -7

Plugging the numbers in the above formula, we have

This agrees with what we calculated directly from the equation of the line!

Hence, slope of the line on the graph = 6

6 0

4 years ago

What is: k–66≤ – 84 in one-step inequalities?

kykrilka [37]

Answer:

$k\le \:-18$

Step-by-step explanation:

First, you add 66 to both sides so then the equation you are trying to solve will be: $k-66+66\le \:-84+66$

Finally, you simplify and get: $k\le \:-18$

Hope this helped!

8 0

2 years ago

Look at the two expressions. 3x−18 3⋅(x−6) Are the two expressions equivalent?

Ivanshal [37]

Yes because if you distribute the 3 and multiply it with 3 • x and 3• 6 you’ll get 3x-18

8 0

3 years ago

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