Mathematics, 13.04.2021 01:30 smarcelle

Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal probability distribution with a mean of 36 hours. hours and a standard deviation of 5.5 hours. As a part of its quality assurance program, Power +, Inc. tests samples of 9 batteries. a. What can you say about the shape of the distribution of the sample mean?
b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)
c. What proportion of the samples will have a mean useful life of more than 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
d. What proportion of the sample will have a mean useful life greater than 34.5 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)
e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours? (Round z value to 2 decimal places and final answer to 4 decimal places.)

Answers: 2

Show answers

Answers

Answer from: ryrytkg8091

a) By the Central Limit Theorem, it is approximately normal.

b) The standard error of the distribution of the sample mean is 1.8333.

c) 0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d) 0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours

e) 0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

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.

Mean of 36 hours and a standard deviation of 5.5 hours.

This means that $\mu = 36, \sigma = 5.5$

a. What can you say about the shape of the distribution of the sample mean?

By the Central Limit Theorem, it is approximately normal.

b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)

Sample of 9 means that n = 9 . So

$s = \frac{\sigma}{\sqrt{n}} = \frac{5.5}{\sqrt{9}} = 1.8333$

The standard error of the distribution of the sample mean is 1.8333.

c. What proportion of the samples will have a mean useful life of more than 38 hours?

This is 1 subtracted by the pvalue of Z when X = 38. So

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

By the Central Limit Theorem

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

$Z = \frac{38 - 36}{1.8333}$

Z = 1.09

Z = 1.09 has a pvalue of 0.8621

1 - 0.8621 = 0.1379

0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d. What proportion of the sample will have a mean useful life greater than 34.5 hours?

This is 1 subtracted by the pvalue of Z when X = 34.5. So

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

$Z = \frac{34.5 - 36}{1.8333}$

Z = -0.82

Z = -0.82 has a pvalue of 0.2061.

1 - 0.2061 = 0.7939

0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.

e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?

pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So

0.8621 - 0.2061 = 0.656

0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

Answer from: Quest

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200. after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes 1800 - 6400 which gets you 11,600.

Answer from: Quest

y=3n + 1

step-by-step explanation:

this is wrong because it says the second number is one less and i added one instead

Another question on Mathematics

Mathematics, 21.06.2019 23:30

Which of the following statements would be sufficient to prove that parallelograms pqrs is a rectangle ?

Answers: 2

Answer

Mathematics, 22.06.2019 00:00

At a local museum, the total price for one adult and one child is $11. mrs. smith paid for herself and her three children. she spent $19. record the system of equations to be solved and then find the price of an adult and child ticket using either elimination or substitution.

Answers: 1

Answer

Mathematics, 22.06.2019 01:10

You work in a hospital that has 9 floors. you need to see 3 patients on each floor. how many patients do you need to see in all?

Answers: 2

Answer

Mathematics, 22.06.2019 02:00

Study published in the journal of personality and individual differences found that adults with adhd displayed more creative achievement than those who didn't have the disorder. "for the same reason that adhd might create problems, like distraction, it can also allow an openness to new ideas," says holly white, assistant professor of cognitive psychology. "not being completely focused on a task lets the mind make associations that might not have happened otherwise." white and priti shah at the university of michigan gave 60 college students â€“ half of them with adhd â€“ a series of tests measuring creativity across 10 domains. the adhd group scored higher across the board. the adhd group showed more of a preference for brainstorming and generating ideas than the non-adhd group, which preferred refining and clarifying ideas. the adhd status of the participants was established by asking whether the individual had ever been clinically diagnosed with adhd/add. the tests of creativity were pencil-and-paper tasks administered in a laboratory setting. each of the ten scales was comprised of multiple questions, the scores on which were summed (e.g., writing creativity: "how many words can you make from the letters in the word 'psychology' invention creativity: "write down as many uses for a paper clip that you can think of.") this procedure does allow for a participant to be scored as showing no creativity under these conditions. a) state the research question in plain language (i wonder if is related to (1 point) b) state the null hypothesis (1 point) c) state the research hypothesis (1 point) d) is the research hypothesis directional or non-directional (1 point) e) name the predictor / independent variable f) give the operational definition of the predictor / independent variable g) evaluate the construct validity of the predictor / independent variable. (face, procedure, method-match) h) name the outcome / dependent variable i) give the operational definition of the outcome / dependent variable. j) evaluate the construct validity of the outcome / dependent variable. (face, procedure, method-match)

Answers: 1

Answer

You know the right answer?

Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batte...

Questions