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To estimate the mean age for a population of 4000 employees, a simple random sample of 40 employees is selected. If the population standard deviation is 8.2 years, computer the standard error of the mean. (Round to one decimal place) What is the probability that the sample mean age of the employees will be within 2 years of the population mean age

Answers

Answer 1

Answer:

Answer:

The standard error of the mean is 1.3.

87.64% probability that the sample mean age of the employees will be within 2 years of the population mean age

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:

$Z = (X - \mu)/(\sigma)$

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 $s = (\sigma)/(√(n))$

In this problem, we have that:

$\sigma = 8.2, n = 40$

Computer the standard error of the mean

$s = (8.2)/(√(40)) = 1.3$

The standard error of the mean is 1.3.

What is the probability that the sample mean age of the employees will be within 2 years of the population mean age

This is the pvalue of Z when $X = \mu + 2$ subtracted by the pvalue of Z when $X = \mu - 2$ . So

$X = \mu + 2$

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem

$Z = (X - \mu)/(s)$

$Z = (\mu + 2 - \mu)/(1.3)$

$Z = 1.54$

$Z = 1.54$ has a pvalue of 0.9382

-----

$X = \mu - 2$

$Z = (X - \mu)/(s)$

$Z = (\mu - 2 - \mu)/(1.3)$

$Z = -1.54$

$Z = -1.54$ has a pvalue of 0.0618

0.9382 - 0.0618 = 0.8764

87.64% probability that the sample mean age of the employees will be within 2 years of the population mean age

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Answers

Answer:

No.

Step-by-step explanation:

3/4 = 0.75

Answer: non-repeating

Step-by-step explanation:

Which number line represents the solutions to |x + 4| = 2?

Answers

Answer:

The solution is represented by the first number line, wich has the solutions x=-6 and x=-2.

Step-by-step explanation:

We have an absolute value function for the equation. This means that we should have two differents solution in the real number line. As the equation is

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when we clear out the absolute value, we will have two possible solutions:

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and

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now we clear x from both equations

$x+4=2 \Leftrightarrow x=2-4 \Leftrightarrow x=-2$

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the first number line

given | x + 4 | = 2

removing the bars from the absolute value gives

x + 4 = 2 or x + 4 = - 2

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5. Expla in why 4 is or is not a multiplicative inverse mod 10 of 7.

Answers

Answer:

4 is not. (3 is)

Step-by-step explanation:

A number is the multiplicative inverse of 7 (mod 10) if the product mod 10 is 1.

7 × 4 mod 10 = 28 mod 10 = 8 . . . . not 1

What is the slope of the line represented by the equation y = - 1/2x + 1/4

Answers

Answer:

The slope is -1/2

Step-by-step explanation:

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define the null and alternative null hypothesis for the following. also, explain what it would mean to make a type 1 error and explain what it would mean to make a type 2 error. the newspaper in a certain city had a circulation of 15,000 per day in 2010. you believe that the newspaper circulation is more than 15,000 today

Answers

Answer:

(A)

Null hypothesis: Newspaper circulation in the city per day was = 15,000 in 2010

(B)

Alternative hypothesis: Newspaper circulation in the city today is > 15,000

(C)

Type 1 Error: This is the rejection of a true null hypothesis. It is the acceptance of the alternative hypothesis when the null hypothesis is true.

(D)

Type 2 Error: This is the non-rejection of a false null hypothesis. It is the acceptance of a null hypothesis when it is false.

Step-by-step explanation:

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Hhgggfgn help hellp
me

Answers

Answer:

First one

Step-by-step explanation:

Answer:

Hey! No need to fret ok so you are doing 7/6 the answer is 1.16 what do we know about this that is true.

Step-by-step explanation:

You are correct only the sum which is 1.16 is irrational because the product of the numbers is rational. Hope I help have a good day please put me for brainliest Thank You!

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