Mathematics, 06.03.2021 14:00 makiahlynn706

Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and a standard deviation of 1.1 ounces. (a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces? Round your answer to 4 decimal places.

(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces? Round your answer to 4 decimal places.

Answers: 1

Show answers

Answers

Answer from: RosaJackson8088

a) 0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

b) 0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

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 zscore 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 pvalue, 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.

Mean of 8.0 ounces and a standard deviation of 1.1 ounces.

This means that $\mu = 8, \sigma = 1.1$

(a) If 5 potatoes are randomly selected, find the probability that the mean weight is less than 9.3 ounces?

n = 5 means that $s = \frac{1.1}{\sqrt{5}} = 0.4919$

This probability is the pvalue of Z when X = 9.3. So

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

By the Central Limit Theorem

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

$Z = \frac{9.3 - 8}{0.4919}$

Z = 2.64

Z = 2.64 has a pvalue of 0.9959

0.9959 = 99.59% probability that the mean weight is less than 9.3 ounces

(b) If 6 potatoes are randomly selected, find the probability that the mean weight is more than 9.0 ounces?

n = 6 means that $s = \frac{1.1}{\sqrt{6}} = 0.4491$

This probability is 1 subtracted by the pvalue of Z when X = 9. So

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

$Z = \frac{9 - 8}{0.4491}$

Z = 2.23

Z = 2.23 has a pvalue of 0.9871

1 - 0.9871 = 0.0129

0.0129 = 1.29% probability that the mean weight is more than 9.0 ounces

Answer from: Quest

the answer is two. hope this !

Answer from: Quest

step-by-step explanation:

659

Another question on Mathematics

Mathematics, 21.06.2019 17:00

Need on this one asap im almost done with this subject

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

Need ! the total ticket sales for a high school basketball game were $2,260. the ticket price for students were $2.25 less than the adult ticket price. the number of adult tickets sold was 230, and the number of student tickets sold was 180. what was the price of an adult ticket?

Answers: 1

Answer

Mathematics, 21.06.2019 20:30

Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (-1+i)+(21+5i)+0

Answers: 2

Answer

Mathematics, 21.06.2019 22:00

Worth 100 points need the answers asap first row -x^2 2x^2 (x/2)^2 x^2 x is less than 2 x is greater than 2 x is less than or equal to 2 x is greater than or equal to 2 second row -5 -5/2 4 5 •2 is less than x& x is less than 4 •2 is less than or equal to x & x is less than or equal to 4 •2 is less than or equal to x& x is less than 4 •2 is less than x& x is less than or equal to 4

Answers: 2

Answer

You know the right answer?

Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.0 ounces and...

Questions

Mathematics, 20.10.2020 02:01

Please help me! i will give u brainliest :0 ...

Mathematics, 20.10.2020 02:01

Please help me I can’t figure it out ...

Mathematics, 20.10.2020 02:01

The circle below is centered at the point (-1,2) and has a radius of length 3. What is its equation? O A. (x-2)2 + (y + 1)2 = 32