Anyone know this? thank you

Which graph represents the compound inequality?

jenyasd209 [6]

Answer:

4th option

Step-by-step explanation:

open circle means more than or less than

n is more than -3 but less than 1

7 0

3 years ago

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

When you add the same number to each side of an equation, do you always get an equivalent equation? webasign?

CaHeK987 [17]

Yes you always do.

eg x - 2 = 8

x - 2 + 2 = 8 + 2

x = 10
if we plug x = 10 into the original equation we se that this fits:-

10 - 2 = 8

8 0

3 years ago

4x + y = 10 7x + 2y = 17

Nezavi [6.7K]

Answer:

x = 3, y = - 2

Step-by-step explanation:

By substitution method,

4x + y = 10 -------> equation 1.

7x + 2y = 17 -------> equation 2.

From equation 1,

y = 10 - 4x ------> equation 3.

Substitute equation 3 in 2,

7x + 2 ( 10 - 4x ) = 17

7x + 20 - 8x = 17

7x - 8x = 17 - 20

- x = - 3

x = 3

Substitute x = 3 in equation 1,

4 ( 3 ) + y = 10

12 + y = 10

y = 10 - 12

y = - 2

Hence,

x = 3

y = - 2

6 0

2 years ago

Read 2 more answers

Order from least to greatest

Orlov [11]

Answer:
In order from least to greatest: 0.25, 3 ⅜, 3 ⅖;

Or, write as: 0.25 < 3 ⅜ < 3 ⅖ .
___________________________________
Explanation:

0.25 = ¼ l (less than "1"); the lowest of the three given values.

The remaining two values have the same whole number of 3, and a fraction:
3 ⅖ ; and 3 ⅜.

The least common multiples among the denominators of the fraction values is 40. ⅖ = ?/40 ; 5*? =40? 5* 8 = 40, so 2*8 = 16;
Thus, ⅖ = 16/40, and 3 ⅖ = 3 16/40. 3/8 = ?/40? 8*5 =40; so 3*5 = 15 ; thus ⅜ = 15/40; and
and 3 ⅜ = 3 15/40.
3 15/40 is less than than 3 16/40;
as such; 3 ⅜ is less than 3 ⅖.

So, in order from least to greatest: 0.25, 3 ⅜, 3 ⅖;
Or, write as: 0.25 < 3 ⅜ < 3 ⅖ .

7 0

3 years ago