How do you know the correct order in which to evaluate algebraic expressions?

A tobacco company claims that the amount of nicotene in its cigarettes is a random variable with mean 2.2 and standard deviation

Aleksandr-060686 [28]

Answer:

0% probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true.

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 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:

$Z = \frac{X - \mu}{\sigma}$

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 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 $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 2.2, \sigma = 0.3, n = 100, s = \frac{0.3}{\sqrt{100}} = 0.03$

What is the approximate probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true?

This is 1 subtracted by the pvalue of Z when X = 3.1. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{3.1 - 2.2}{0.03}$

$Z = 30$

$Z = 30$ has a pvalue of 1.

1 - 1 = 0

0% probability that the sample mean would have been as high or higher than 3.1 if the company’s claims were true.

4 0

4 years ago

Which one is correct

Alexandra [31]

Answer:

i believe its false good Sir

6 0

3 years ago

Read 2 more answers

Which figured demonstrates a translation?

natulia [17]

the one where they are diagonal from one another

8 0

3 years ago

A recipe calls for 2 1/2 Cups of flour and four eggs. If only three eggs are used, how many cups of flour should be used? Give y

MAXImum [283]

Answer:

Step-by-step explanation: write the equation in the form of a proportion

2 1/2 is to 4 as something is to 3

2 1/2 / 4 = x/3

Then, cross multiply 2 1/2 x 3 or

5/2 x 3/1 = 15/2

Next cross multiply 4•X= 4X

Write as 4X = 15/2

Divide both sides by 4.

4X/ 4 = 15/2 /4

x = 15/2÷ 4/1

Divide by changing the sign to multiplication and inverting 4/1 to 1/4 like this:. 15/2. × 1/4= 15/8

Finally, 15/8 simplifies to 1 7/8 cups

8 0

3 years ago

Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below

Anastaziya [24]

Answer:

Nico

Step-by-step explanation:

In order to compare who had the best performance on the aptitude test, we can use Z score. Z score indicates how many standard deviation a result is over the mean. For this case the higher the result is, the best is the performance on the aptitude test.

Z score is expressed with the following formula:

Z=(X-μ)/σ

Where:

X is the test score

µ is the mean

σ is the standard deviation

Replacing in the formula we obtained

For Nico:

X = 88.3

µ = 66.2

σ = 13

Z=(88.3-66.2)/13=1.7

For Justin:

X = 226.2

µ = 216

σ = 17

Z=(226.2-216)/17=0.6

For Tera:

X = 7.97

µ = 7.2

σ = 0.7

Z=(7.97-7.2)/0.7=1.1

Nico had the higher Z score which means he had the better performance on the test and he should be offered the job.

3 0

3 years ago