8 y and y are like terms. True or False

Based on historical data, your manager believes that 37% of the company's orders come from first-time customers. A random sample

fomenos

Answer:

0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38

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 estabilishes 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

37% of the company's orders come from first-time customers.

This means that $p = 0.37$

A random sample of 225 orders will be used to estimate the proportion of first-time-customers.

This means that $n = 225$

Mean and standard deviation:

$\mu = p = 0.37$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.37*0.63}{225}} = 0.0322$

What is the probability that the sample proportion is between 0.26 and 0.38?

This is the pvalue of Z when X = 0.38 subtracted by the pvalue of Z when X = 0.26.

X = 0.38

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

By the Central Limit Theorem

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

$Z = \frac{0.38 - 0.37}{0.0322}$

$Z = 0.31$

$Z = 0.31$ has a pvalue of 0.6217

X = 0.26

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

$Z = \frac{0.26 - 0.37}{0.0322}$

$Z = -3.42$

$Z = -3.42$ has a pvalue of 0.0003

0.6217 - 0.0003 = 0.6214

0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38

5 0

2 years ago

A corporate team is hosting a fundraising event. It cost them $145 to book the venue, but they are selling the tickets to the ev

ankoles [38]

Answer:

They must sell 43 tickets to raise $500

Step-by-step explanation:

Cost to book the venue = $145

-145 plus 500 (money they need to raise) = $645

Each ticket costs $15

645/15 = 43 tickets

8 0

3 years ago

The anithistamine Benadryl is often prescribed for allergies. A typical dose for a 100-pound person is 25 mg every six hours. Fo

Firdavs [7]

Answer:

56 chewable tablets

280mL liquid Benadryl

Step-by-step explanation:

For the first part:

First we need to find out how many tablets of 12.5mg would we need per dose.

1 dose is 25 mg and the tablets are in 12.5 mg form.

$1 dose = \dfrac{25mg}{12.5mg} = 2$

That would mean you would need 2 tablets per dose.

Next you need to calculate how many times a day it needs to be taken. A day has 24 hours and it needs to be taken every 6 hours. Just divide 24 hours by 6 hours. So that would mean that it needs to be taken 4 times a day.

Next we need to see how many times a week it should be taken and you can get that by multiplying the number of times a day by the number of days a week.

4 x 7 = 28 times

Lastly, you multiply the number of times a week by the number of tablets per dose.

28 times a week x 2 tablets = 56 tablets.

For the second part:

12.5 mg/5mL

The needed dose is 25 mg so we need to find how many mL is needed for 25 mg. 12.5mg is only have of 25 mg we need to double it to attain the correct dosage.

$\dfrac{12.5mg}{5mL}$ x $\dfrac{2}{2}$ = $\dfrac{25mg}{10mL}$

This means that for every 25 mg, you will need to give 10mL.

Again we do the same procedure as the first to decide how much liquid Benadryl you need to give in a week. We know that based on the previous that we need to administer this 28 times a week, so just multiply the number of mL per dose by the number of times per week.

10mL x 28 = 280mL

4 0

3 years ago

A house cast a 10 foot shadow. A 5 foot boy castsa 4 foot shadow.

krok68 [10]

11 feet I think, hope this helps

7 0

3 years ago

Pls help asap!! Hhuwdqnjwl

vampirchik [111]

Answer:

14