<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B5%7D%20%3D%2027" id="TexFormula1" title=" \frac{x}{5} = 27" alt=" \frac{x}

Using the normal distribution and the central limit theorem, it is found that there is a 0.1635 = 16.35% probability of a sample result with 68% or fewer returns prior to the third day.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

It 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, which is the percentile of X.
By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportions has mean $\mu = p$ and standard error $s = \sqrt{\frac{p(1 - p)}{n}}$

In this problem:

Sample of 500 customers, hence $n = 500$ .

Amazon believes that the proportion is of 70%, hence $p = 0.7$

The mean and the standard error are given by:

$\mu = p = 0.7$

$s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.7(0.3)}{500}} = 0.0205$

The probability is the p-value of Z when X = 0.68, hence:

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

By the Central Limit Theorem

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

$Z = \frac{0.68 - 0.7}{0.0205}$

$Z = -0.98$

$Z = -0.98$ has a p-value of 0.1635.

0.1635 = 16.35% probability of a sample result with 68% or fewer returns prior to the third day.

A similar problem is given at brainly.com/question/25735688

7 0

2 years ago

An animal shelter has 9/10 of its crates filled with animals. 1/2 if the filled crates are holding dogs. What fraction of the to

quester [9]

4/10 or 2/5 because 1/2 is 5/10 and 9/10-5/10=4/10

3 0

4 years ago

Read 2 more answers

Find the area of the circle. Round your answer to the nearest hundredth with 3in i really need help

REY [17]

Answer:

The area of the circle with a 3-inch diameter is 7.07 square inches.

Step-by-step explanation:

The formula for the area of a circle is

A = πr²

If you are given diameter, take half of that to get the radius: 3 ÷ 2 = 1.5

Then take the radius, 1.5 and square it (multiply by itself) 1.5 × 1.5 = 2.25

Then multiply r² times pi. You can use 3.14. (sometimes you will need 3.14159)

2.25 × 3.14 = 7.065

Your instructions are to "round to the nearest hundredth" so you look to the thousandth place and see a 5. Rules fro rounding: "If the number is 5 or higher, add 1 to the place you are rounding to. If 4 or less, leave the place as it is."

You see a 6 in the hundredths place. Add 1. so the rounded answer is 7.07.

Then you put in the units measure. Inches are given, so the Area will be square inches

7.07 in²

3 0

3 years ago