I need help with this worksheet, if u don't know the answer please no reply please :(

The number of years of education of self-employed individuals in the united states has a population mean of 13.6 years and a pop

muminat

Answer:

0.3 years

Step-by-step explanation:

With problems like these, I always like to start by breaking down the information into smaller pieces.

μ = 13.6

σ = 3.0

Survey of 100 self-employed people

(random variable) X = # of years of education

So now we have some notation, where μ represents population mean and σ represents population standard deviation. Hopefully, you already know that the sample mean of x-bar is the same as the population mean, so x-bar = 13.6. Now, the question asks us what the standard deviation is. Since the sample here is random, we can use the Central Limit Theorem, which allows us to guess that a distribution will be approximately normal for large sample sizes (that is, n ≥ 30). In this case, our sample size is 100, so that is satisfied. We're also told our sample is random, so we're good there, too. Now all we have to do is plug some stuff in.

The Central Limit Theorem says that for large values of n, x-bar follows an approximately normal distribution with sample mean = μ and sample standard deviation = σ/√n. So, with that info, all we need to do to find the standard deviation of x-bar is to plug our σ and n into the above formula.

σ(x-bar) = σ/√n

σ(x-bar) = 3.0/√100

σ(x-bar) = 0.3

So your answer here is .3 years.

7 0

3 years ago

Stephanie just redecorated her bedroom. She wants to paint her door green but needs to know the surface area of the door to see

Alona [7]

Answer:The surface area of the door is 33,680

Step-by-step explanation:

The answer is correct.

3 0

3 years ago

The measures of the sides of a triangle are 2x + 3, 8x – 4, and . Write an expression that describes the perimeter of the triang

tresset_1 [31]

Answer:

C

Step-by-step explanation:

Perimeter of a triangle is the sum of all the sides.

A triangle has 3 sides, so if we add up all the 3 sides lengths (given as expressions here) of the triangle, we will have the perimeter.

Perimeter = $(2x+3)+(8x-4)+(x^2)\\=2x+3+8x-4+x^2$

Now combining like terms we have:

$2x+3+8x-4+x^2\\=x^2+10x-1$

Answer choice C is the correct one.

4 0

3 years ago

A filling machine fills bottles of nail polish with amounts that are normallydistributed with mean 18 mL and standard deviation

natulia [17]

Answer:

a. 0.2033 = 20.33% probability that one of the randomly selected bottles is filled with less than 17.5mL of nail polish

b. 0.0019 = 0.19% probability that the average fill of the twelve bottles is more than 17.5mL

Step-by-step explanation:

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

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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 $s = \frac{\sigma}{\sqrt{n}}$ .