Solve Quadratically:<br><br> ║x+2║=2.3

A distribution of values is normal with a mean of 60 and a standard deviation of 16. From this distribution, you are drawing sam

professor190 [17]

Answer:

The interval containing the middle-most 76% of sample means is between 56.24 and 63.76.

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

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

A distribution of values is normal with a mean of 60 and a standard deviation of 16.

This means that $\mu = 60, \sigma = 16$

Samples of size 25:

This means that $n = 25, s = \frac{16}{\sqrt{25}} = 3.2$

Find the interval containing the middle-most 76% of sample means.

Between the 50 - (76/2) = 12th percentile and the 50 + (76/2) = 88th percentile.

12th percentile:

X when Z has a p-value of 0.12, so X when Z = -1.175.

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

By the Central Limit Theorem

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

$-1.175 = \frac{X - 60}{3.2}$

$X - 60 = -1.175*3.2$

$X = 56.24$

88th percentile:

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

$1.175 = \frac{X - 60}{3.2}$

$X - 60 = 1.175*3.2$

$X = 63.76$

The interval containing the middle-most 76% of sample means is between 56.24 and 63.76.

3 0

3 years ago

This table shows the ratio of daisies to roses.

podryga [215]

Answer:

To find the values in each row, divide the values in the previous row by 4

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Katie invested a total of $4000, part at 2% simple interest and part at 3% simple interest. At the end of 1 year, the inves

Fiesta28 [93]

Answer:

$3000

$1000

Step-by-step explanation:

the formula for simple interest = principal x time x interest rate

let the amount invested in the 2% investment be a

let the amount invested in the 3% investment be (4000 - a)

(a x 0.02 x 1) + ([4000 - a] x 0.03 x 1) = $90

0.02a + 120 - 0.03a = 90

Collect like terms and solve for a

0.01a = 30

a = $3000

The amount invested in the 3% investment be (4000 - a) = $4000 - $3000 = $1000

7 0

3 years ago

Can someone please explain how to find the answer? My old teacher didn’t do it this way and I’m lost :/

Valentin [98]

Answer:

the triangle means "change in". so triangle x means the change in the x values and triangle y means change in y values so yeah mental calculate the difference

4 0

3 years ago

Cell phone usage differs by gender. The role of cell phone in modern life was investigated by Pew Internet and American life pro

ahrayia [7]

Answer:

A) Two populations: American men and American women, as it estimated from the broad of the survey.

B) The proportion of men that sometimes do not drive safely while talking or texting on cell phone is 32%, and the proportion of women that sometimes do not drive safely while talking or texting on cell phone is 25%.

C) There is enough evidence to support the claim that the proportion of men and women who used their cell phone in an emergency differ significantly (P-value=0.014).

Step-by-step explanation:

A. We have two populations: American men and American women. This are the populations from which we want to infere the difference of means.

B. The estimation of the proportion is already shown in the question:

The proportion of men that sometimes do not drive safely while talking or texting on cell phone is 32%, and the proportion of women that sometimes do not drive safely while talking or texting on cell phone is 25%.

These are unbiased estimators of the populations proportions.

C. This is a hypothesis test for the difference between proportions.

The claim is that the proportion of men and women who used their cell phone in an emergency differ significantly.

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0$

The significance level is 0.05.

The sample 1 (men), of size n1=643 has a proportion of p1=0.71.

The sample 2 (women), of size n2=643 has a proportion of p2=0.77.

The difference between proportions is (p1-p2)=-0.06.

$p_d=p_1-p_2=0.71-0.77=-0.06$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{457+495.11}{643+643}=\dfrac{952}{1286}=0.7403$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.7403*0.2597}{643}+\dfrac{0.7403*0.2597}{643}}\\\\\\s_{p1-p2}=\sqrt{0.0003+0.0003}=\sqrt{0.0006}=0.0245$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.06-0}{0.0245}=\dfrac{-0.06}{0.0245}=-2.45$

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

$P-value=2\cdot P(z$

As the P-value (0.014) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of men and women who used their cell phone in an emergency differ significantly.

3 0

4 years ago

Solve Quadratically: ║x+2║=2.3