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Korvikt [17]
3 years ago
8

The selling price for houses in a neighborhood in West Richland, WA have an approximately normal distribution with a mean sellin

g price of $275,000 and a standard deviation of $10,500. If 35 homes sell in this neighborhood, what is the probability that the average selling price of the 35 homes will be within $2000 of the true mean (that is, what is the probability the sample mean will be between $273,000 and $277,000)
Mathematics
1 answer:
Liula [17]3 years ago
3 0

The probability that the average selling price of the 35 homes will be within $2000 of the true mean is 0.5753

First, we need to find the z-score and this is expressed according to the formula;

z=\dfrac{x-\mu}{\sigma}

x is the sample space

\mu is the mean value

\sigma is the standard deviation

Given the following parameters

Mean = $275,000

Standard deviation = $10,500

If the true mean is $273,000, then;

z=\dfrac{273,000-275000}{10,500} \\z = \frac{-2000}{10500}\\z= -0.1905

If the true mean is $277,000

z=\dfrac{277,000-275000}{10,500} \\z = \frac{2000}{10500}\\z= 0.1905

This means that the z-score is between -0.1095 and 0.1095

Pr( -0.1095 ≤ z ≤ 0.1095)

According to the z table, the probability that the average selling price of the 35 homes will be within $2000 of the true mean is 0.5753

Learn more here: brainly.com/question/17436641

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