Mathematics, 20.03.2020 12:38 adamske0

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 35,869 miles, with a variance of 12,194,060. What is the probability that the sample mean would differ from the population mean by less than 375 miles in a sample of 269 tires if the manager is correct? Round your answer to four decimal places.

Answers: 1

Show answers

Answers

Answer from: ooof3

0.9216 = 92.16% probability that the sample mean would differ from the population mean by less than 375 miles in a sample of 269 tires if the manager is correct

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 normally distributed samples 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

The standard deviation is the square root of the variance. So

$\mu = 35869, \sigma = \sqrt{12194060} = 3492, n = 269, s = \frac{3492}{\sqrt{269}} = 212.9$

What is the probability that the sample mean would differ from the population mean by less than 375 miles in a sample of 269 tires if the manager is correct?

This is the pvalue of Z when X = 35869 + 375 = 36244 subtracted by the pvalue of Z when X = 35869 - 375 = 35494.

X = 36244

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

By the Central Limit Theorem

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

$Z = \frac{36244 - 38569}{212.9}[tez]Z = 1.76$

[tez]Z = 1.76[/tex] has a pvalue of 0.9608

X = 35494

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

$Z = \frac{35494 - 38569}{212.9}[tez]Z = -1.76$

[tez]Z = -1.76[/tex] has a pvalue of 0.0392

0.9608 - 0.0392 = 0.9216

0.9216 = 92.16% probability that the sample mean would differ from the population mean by less than 375 miles in a sample of 269 tires if the manager is correct

Answer from: Quest

sorry not sure

step-by-step explanation:

Answer from: Quest

A=bxh3.2x1.8=5.76 centimeters square

Another question on Mathematics

Mathematics, 21.06.2019 20:10

Over which interval is the graph of f(x) = x2 + 5x + 6 increasing?

Answers: 1

Answer

Mathematics, 21.06.2019 23:10

In which quadrant does the point lie? write the coordinates of the point. a. quadrant ii; (–2, –4) b. quadrant iii; (2, 4) c. quadrant iii; (–2, –4) d. quadrant iv; (–4, –2)

Answers: 3

Answer

Mathematics, 22.06.2019 01:50

Our star pitcher, foster enlight, can throw a pitch so fast that it gets to the catcher’s mitt before it leaves foster’s fingers! if the team wins a game then the probability that foster was pitching is 0.8 but only if foster had at least one day’s rest since his last pitching assignment. if foster does not have a day off and the team still wins, the probability that foster was pitching drops by half of what it was on the previous day. if the team wins three games in succession from the toronto tachyons and foster pitched in game #2, what is the probability that he pitched in one or more of the other games? (assume that foster did not pitch on the day before the first game of this three game series.)

Answers: 1

Answer

Mathematics, 22.06.2019 03:30

More challenges: 1) factor out the indicated quantity.8mn² + 7mn - m : factor out the quantity -m2) factor the polynomial by grouping.2vw + 7cv + 14cw + 49c²3) factor completely using the difference of squares along with factoring by grouping.25v³ - 25v² - 4v + 44) factor the sum of cubes. 125x³ + 645) q³ + 27r³6) factor completely. use difference of squares.729p^6 - 6^67) solve the equation(7x + 4)(9x - 1) = 08) a. find the values of x for which f (x) = 0b. find f (0)f (x) = x² + 2x - 489) find the x and y-intercepts for the function defined by y = f (x)f (x) = (x + 3)(x + 4)(x - 1)²10) factor the trinomial completely by using any method. remember to look for a common factor first. 3v² - 2v - 16

Answers: 2

Answer

You know the right answer?

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 35...

Questions