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Zina [86]
2 years ago
10

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 48,564 miles, with a standard

deviation of 3293 miles. What is the probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct? Round your answer to four decimal places.
Mathematics
1 answer:
DerKrebs [107]2 years ago
6 0

Answer:

0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 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:

\mu = 48564, \sigma = 3293, n = 281, s = \frac{3293}{\sqrt{281}} = 196.44

What is the probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct?

This is the pvalue of Z when X = 48101. So

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

By the Central Limit Theorem

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

Z = \frac{48101 - 48564}{196.44}

Z = -2.36

Z = -2.36 has a pvalue of 0.0091

0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct

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Answer:

Step-by-step explanation:

cartesian plane :

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(-2,4)......we have x is negative and y is positive...so we are in quadrant 2

(3,-1)....we have x is positive and y is negative...in quadrant 4

(-1,0) ...if u have a 0 in ur points, they do not lie in any quadrant because they are located on an axis....this is located on axis x

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3 years ago
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Answer:

C) 15

Step-by-step explanation:

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Plug in n = 6 and r =2, in the above formula, we get

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i dont have time to do all of it (sorry)

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Answer:

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irinina [24]

Answer:

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