Mathematics, 19.02.2020 21:24 janiyahmcgolley

The distribution of weights of United States pennies is approximately normal with a mean of 2.5 grams and a standard deviation of 0.03 grams.

a. What is the probability that a randomly chosen penny weights less than 2.4 grams?

b. Describe the sampling distribution of the mean weight of 10 randomly chosen pennies.

c. What is the probability that the mean weight of 10 pennies is less than 2.4 grams?

d. Sketch the two distributions (population and sampling) on the same scale.

e. Could you estimate the probabilities from (a) and (c) if the weights of the pennies had a skewed distribution?

Answers: 3

Show answers

Answers

Answer from: lashaaungas

a) P(X

b) Since the distribution for X is normal then the distribution for the sample mean $\bar X$ is also normal and given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\mu_{\bar X}=2.5$

$\sigma_{\bar X}=\frac{0.03}{\sqrt{10}}=0.00949$

c) $P(\bar X$

We can use the z score formula given by $z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And using the z score formula we got:

$P(\bar X$

d) Figure attached.

As we can see we have less deviation for the sample mean and for this reason we have more values near to the mean.

e) Since we just have the mean and the deviation we can't estimate the probability if we don't know the distribution.

The z score can't be applied if we have a normal distribution.

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(2.5,0.03)$

Where $\mu=2.5$ and $\sigma=0.03$

And we want this probability:

P(X

We can use the z score formula given by $z = \frac{x -\mu}{\sigma}$

And using the z score formula we got:

P(X

Part b

Since the distribution for X is normal then the distribution for the sample mean $\bar X$ is also normal and given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\mu_{\bar X}=2.5$

$\sigma_{\bar X}=\frac{0.03}{\sqrt{10}}=0.00949$

Part c

$P(\bar X$

We can use the z score formula given by $z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And using the z score formula we got:

$P(\bar X$

Part d

Figure attached.

As we can see we have less deviation for the sample mean and for this reason we have more values near to the mean.

Part e

Since we just have the mean and the deviation we can't estimate the probability if we don't know the distribution.

The z score can't be applied if we have a normal distribution.

The distribution of weights of United States pennies is approximately normal with a mean of 2.5 gram

Answer from: Quest

4038 is the answer lol just use a calculator

Answer from: Quest

i dony know

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 22:00

Liz is shipping a package to her friend. the maximum weight of a medium flat-rate box is 20 pounds, including the box which weighs 6 ounces. write and solve an inequality to describe the possible weight in pounds, w, of the contents that liz will ship to her friend if she must use a medium flat-rate box. use the drop-down menus to explain your answer.

Answers: 2

Answer

Mathematics, 21.06.2019 23:30

Graham’s monthly bank statement showed the following deposits and withdrawals. -$25.20, $42.75, -$22.04, -$18.50, $74.11. part a if grahams baldness in the account was $37.86 at the beginning of the month,! 27/4! 2// the account balance at the end of the month? ? plz i will give you 100 points

Answers: 1

Answer

Mathematics, 22.06.2019 00:30

Can someone me immediately, this is due by midnight! if you can't see the question, i'll text it to you. show the steps you took to get your answer.

Answers: 2

Answer

Mathematics, 22.06.2019 02:20

Asalesperson has january sales of $20,000(1,$20,000) and april sales of $80,000 (4,$80,000). what is the rate of change?

Answers: 1

Answer

You know the right answer?

The distribution of weights of United States pennies is approximately normal with a mean of 2.5 gram...