Can you please help me

A sample of size 6 will be drawn from a normal population with mean 61 and standard deviation 14. Use the TI-84 Plus calculator.

AVprozaik [17]

Answer:

$X \sim N(61,14)$

Where $\mu=61$ and $\sigma=14$

Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:

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

$\mu_{\bar X} = 61$

$\sigma_{\bar X}= \frac{14}{\sqrt{6}}= 5.715$

So then is appropiate use the normal distribution to find the probabilities for $\bar X$

Step-by-step explanation:

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". The letter $\phi(b)$ is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: $\phi(b)=P(z$

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:

$X \sim N(61,14)$

Where $\mu=61$ and $\sigma=14$

Since the distribution for X is normal then the distribution for the sample mean $\bar X$ is also normal and given by:

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

$\mu_{\bar X} = 61$

$\sigma_{\bar X}= \frac{14}{\sqrt{6}}= 5.715$

So then is appropiate use the normal distribution to find the probabilities for $\bar X$

8 0

3 years ago

3a + 4n + 5a 3 - 8n + 11

KonstantinChe [14]

Answer:

8a-4n+14?

Step-by-step explanation:

6 0

3 years ago

Please hurry!!

scoray [572]

Answer:

y + 1 = 2(x+1)

Step-by-step explanation:

hope this helps

4 0

3 years ago

A new sweater costs $15.99. If the sweater is on sale for 1/4 off

Mrac [35]

the sweater costs $15.99 regularly, however today is on sale, 1/4 off the regular price, how much is 1/4 of 15.99? well just their product, 15.99 * (1/4) = 3.9975.

that means that just for today, the sweater costs 15.99 - 3.9975.

so, today you're not really paying $15.99 for the sweater, you're paying 3.9975 less, so you're saving 3.9975. That's $3.9975 that you won't be spending on it, thus saving it.

6 0

4 years ago

Read 2 more answers

Meg walks to school and work each day and wants to track how far she walks each day. In the morning, Meg walks 7 blocks due east

worty [1.4K]

Answer:

I am pretty sure it is 19 blocks because it is 14 blocks before going back home. She needs to walk 3 blocks west and 2 blocks south. 14+3+2=19

Step-by-step explanation:

6 0

3 years ago