Hey I need this answer simplified can someone help me?

A student received a coupon for 11% off the total purchase price at a clothing store. Let z be the

Gnom [1K]

Answer: 0.89z

Think of it like 100% - 11% = 89%

You save 11%, so you need to pay the remaining 89%

Taking 89% of z then leads to 0.89z

So that's why z - 0.11z = 0.89z

6 0

3 years ago

The Pew Research Center has conducted extensive research on the young adult population (Pew Research website, November 6, 2012).

Rudik [331]

Answer:

a) $0.93 - 1.96\sqrt{\frac{0.93(1-0.93)}{500}}=0.908$

$0.93 + 1.96\sqrt{\frac{0.93(1-0.93)}{500}}=0.952$

The 95% confidence interval would be given by (0.908;0.0.952)

b) $0.21 - 2.58\sqrt{\frac{0.21(1-0.21)}{500}}=0.163$

$0.21 + 2.58\sqrt{\frac{0.21(1-0.21)}{500}}=0.257$

The 99% confidence interval would be given by (0.163;0.0.257)

c) The margin of error for part a is:

$ME= 1.96\sqrt{\frac{0.93(1-0.93)}{500}}=0.0224$

And for part b is:

$ME=2.58\sqrt{\frac{0.21(1-0.21)}{500}}=0.0470$

So then the margin of error is larger for part b.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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 population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.93 - 1.96\sqrt{\frac{0.93(1-0.93)}{500}}=0.908$

$0.93 + 1.96\sqrt{\frac{0.93(1-0.93)}{500}}=0.952$

The 95% confidence interval would be given by (0.908;0.0.952)

Part b

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.21 - 2.58\sqrt{\frac{0.21(1-0.21)}{500}}=0.163$

$0.21 + 2.58\sqrt{\frac{0.21(1-0.21)}{500}}=0.257$

The 99% confidence interval would be given by (0.163;0.0.257)

Part c

The margin of error for part a is:

$ME= 1.96\sqrt{\frac{0.93(1-0.93)}{500}}=0.0224$

And for part b is:

$ME=2.58\sqrt{\frac{0.21(1-0.21)}{500}}=0.0470$

So then the margin of error is larger for part b.

7 0

3 years ago

Whats the median number mode and mean for 95, 97, 100, 86, 78, 96

Naya [18.7K]

Answer:

Mean = 92

Median = 95.5

There is no mode.

What is mean, median, and mode?

Mean, median, and mode are terms in math when it comes to looking at charts and sets/groups of numbers.

1. The mean is the average of a data set.

2. The median is the middle of a data set.

3. The mode is the most common number in a data set.

Mean is found by adding the numbers and dividing the sum by the number of numbers in the list. This is what is most often meant by an average. The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list.

Before we start, let's put the set of numbers in order from least to greatest,

95, 97, 100, 86, 78, 96

78, 86, 95, 96, 97, 100

Now that we have done that let's find the mean,

78 + 86 + 95 + 96 + 97 + 100 = 552

There are 6 numbers in this set so we need to divide 552 by 6,

552 ÷ 6 = 92

92 is the mean/average of this data set,

Now let's find the median,

If we take a look at the data set we can see that there are two numbers in the middle because there are 6 in total,

78, 86, 95, 96, 97, 100

Because there are two values that are in the middle we need to add them up and divide the sum of them by 2,

95 + 96 = 191

191 ÷ 2 = 95.5

95.5 is the median of this data set,

Now let's find the mode,

If we take a look at the date set we can see that none of the numbers are repeated,

So this means there is no mode to this data set,

Therefore the mean is 92, the median is 95.5, and there is no mode.

4 0

2 years ago

A rectangle has a length of 10ft.and a width of 6ft.whats the perimeter

Delicious77 [7]

Add 10 + 10 + 6 + 6 = 32
32 ft.

5 0

4 years ago

Read 2 more answers

A kilometer is more than one-half mile.<br> true<br> false

murzikaleks [220]

I think true...i might be wrong

5 0

3 years ago