Mathematics, 23.06.2021 04:40 Faber9714

from first-time customers. A random sample of 161 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.35 and 0.45

Answers: 3

Show answers

Answers

This probability that the sample proportion is between 0.35 and 0.45 is the p-value of $Z = \frac{0.45 - \mu}{\sqrt{\frac{p(1-p)}{160}}}$ subtracted by the p-value of $Z = \frac{0.35 - \mu}{\sqrt{\frac{p(1-p)}{160}}}$ . These p-values are found looking at the z-table.

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.

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 $s = \sqrt{\frac{p(1-p)}{n}}$

Estimate of the proportion:

This is p, and thus, we use $\mu = p$ .

Sample of 160

This means that:

$n = 160, s = \sqrt{\frac{p(1-p)}{160}}$

What is the probability that the sample proportion is between 0.35 and 0.45?

Answer from: Quest

with btw u said 100pts but it clearly says

i answerd and just got 10pts

no hate

Answer from: Quest

answer: rotate 270° clockwise about (7, 1) and reflect across the line x = 7

step-by-step explanation:

because i took test

Identify the transformation that maps the figure with center (7, 1) onto itself. a) rotate 180° cloc

Another question on Mathematics

Mathematics, 21.06.2019 17:00

Acylinder has volume 45π and radius 3. what is it’s height?

Answers: 2

Answer

Mathematics, 21.06.2019 20:10

Gexpressions: practice question 3 of 5 jackson wants to study the popularity of his music video by tracking the number of views the video gets on his website. the expression below represents the total number of views that jackson's video receives n days after he begins tracking the nu views, where b is the rate at which the number of views changes. alb)" select the statement that would accurately describe the effect of tripling a, the initial number of views before jackson beginst the rate at which the number of views changes, b, will triple. the total number of views the video has after n days, a(b)", will not change. the total number of days since jackson begins tracking views, n, will be reduced by one-third. the total number of views the video has after n days, alb)", will triple. submit

Answers: 3

Answer

Mathematics, 21.06.2019 20:40

Describe the symmetry of the figure. identify lines of symmetry, if any. find the angle and the order of any rotational symmetry.

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

Given the expression (7 ? 4i) ? (2 + 6i), perform the indicated operation and write the answer in the form a + bi.

Answers: 1

Answer

You know the right answer?

from first-time customers. A random sample of 161 orders will be used to estimate the proportion of...