For which of the following conditions will the sum of integers m and n always be an odd integer?

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 33,208 miles, with a standard

avanturin [10]

Answer:

There is a 92.32% probability that the sample mean would differ from the population mean by less than 633 miles in a sample of 49 tires if the manager is correct.

Step-by-step explanation:

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 $\sigma$ , a large sample size 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 operation manager at a tire manufacturing company believes that the mean mileage of a tire is 33,208 miles, with a standard deviation of 2503 miles.

This means that $\mu = 33208, \sigma = 2503$ .

What is the probability that the sample mean would differ from the population mean by less than 633 miles in a sample of 49 tires if the manager is correct?

This is the pvalue of Z when $X = 33208+633 = 33841$ subtracted by the pvalue of Z when $X = 33208 - 633 = 32575$

By the Central Limit Theorem, we have t find the standard deviation of the sample, that is:

$s = \frac{\sigma}{\sqrt{n}} = \frac{2503}{\sqrt{49}} = 357.57$

So

X = 33841

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

$Z = \frac{33841 - 33208}{357.57}$

$Z = 1.77$

$Z = 1.77$ has a pvalue of 0.9616

X = 32575

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

$Z = \frac{32575- 33208}{357.57}$

$Z = -1.77$

$Z = -1.77$ has a pvalue of 0.0384.

This means that there is a 0.9616 - 0.0384 = 0.9232 = 92.32% probability that the sample mean would differ from the population mean by less than 633 miles in a sample of 49 tires if the manager is correct.

4 0

3 years ago

Find vÌ, the orthogonal projection of v onto w. you can't enter vÌ as a variable name in matlab, so call it vbar instead. also c

lubasha [3.4K]

Jjjjjjjjjjjjjjjjjjjj

8 0

3 years ago

Which statement is true

liberstina [14]

B is true
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8 0

3 years ago

Ryan planted 125 trees on my tree farm 28% of rum or maple trees and the rest of them are pine trees. Kioshi helped plant 125 tr

VashaNatasha [74]

Answer:

Ryan planted more maple trees than Kioshi.

Step-by-step explanation:

Given:

Total number of tress planted by Ryan = 125

Percent of maples tree planted by Ryan = 28%

Total number of tress planted by Kioshi = 125

We need to find who planted more maple trees.

Solution:

First we will find the number of maple tree planted by Ryan.

So we can say that;

the number of maple tree planted by Ryan is equal to Percent of maples tree planted by Ryan multiplied by Total number of tress planted by Ryan and then divided by 100.

framing in equation form we get;

the number of maple tree planted by Ryan = $\frac{28}{100}\times 125 = 35$