Statements and reasonings 2(4x+2)=20

A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12. Find the pr

Gre4nikov [31]

Answer:

$z= \frac{47 -50}{\frac{12}{\sqrt{36}}}=-1.5$

$z= \frac{53 -50}{\frac{12}{\sqrt{36}}}=1.5$

And using a calculator, excel ir the normal standard table we have that:

$P(47 \leq \bar X \leq 53) =P(-1.5 \leq Z \leq 1.5)$

And we can calculate the probability like this: $P(-1.5 \leq Z \leq 1.5) = P(z$ Step-by-step explanation:

A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12. Find the probability that the sample mean is in the interval 47<=X<53. Is the assumption of normality important. Why?

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(50,12)$

Where $\mu=50$ and $\sigma=12$

Since the distribution for X is normal then we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

We can find the probability required like this:

$z= \frac{47 -50}{\frac{12}{\sqrt{36}}}=-1.5$

$z= \frac{53 -50}{\frac{12}{\sqrt{36}}}=1.5$

And using a calculator, excel ir the normal standard table we have that:

$P(47 \leq \bar X \leq 53) =P(-1.5 \leq Z \leq 1.5)$

And we can calculate the probability like this:

$P(-1.5 \leq Z \leq 1.5) = P(z$

4 0

1 year ago

Let x stand for the length of an individual screw. 100 screws were sampled at a time. The population mean is 2.5 inches and the

goldfiish [28.3K]

Answer:

The mean is defining the average length(2.5in) of the 100 measured screws.

Step-by-step explanation:

The mean is usually calculated in order to determine the average of a set of values.

8 0

1 year ago

A polling agency reported that 66 percent of adults living in the United States were satisfied with their health care plans. The

Tpy6a [65]

Answer:

A) The probability is 0.95 that the percent of adults living in the United States who are satisfied with their health care plans is between 63.6% and 68.4%.

Step-by-step explanation:

A polling agency reported that 66 percent of adults living in the United States were satisfied with their health care plans. The estimate was taken from a random sample of 1,542 adults living in the United States, and the 95 percent confidence interval for the population proportion was calculated as (0.636, 0.684).

This means that we are 95% sure that the true proportion of adults living in the United States who were satisfied with their health care plans is between 0.636 and 0.684.

So the correct answer is:

A) The probability is 0.95 that the percent of adults living in the United States who are satisfied with their health care plans is between 63.6% and 68.4%.

7 0

1 year ago

On an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two grades was 138. Find the lo

miv72 [106K]

you could use this equation to help you solve it;

x + (x + 42) = 138

the first step is to combine like terms;

2x = 138 -42

2x = 96

X = 96/2

X = 48

we already solved for x now substitute it in the equation I gave you.

48 + (48 + 42) = 138

48 + 90 = 138

hope it helped...if you have any concerns just let me know:)

3 0

2 years ago

-5 + 3g + (-3) - 8g = -18

Greeley [361]

Answer:

the answer is g=2

Step-by-step explanation:

hope this helps!!!

3 0

1 year ago