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Sagot :
Using the normal distribution, it is found that 2.15% of bedroom apartments in the city cost between $750 and $1,000.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
[tex]\mu = 1500, \sigma = 250[/tex]
The proportion of apartments that cost between $750 and $1,000 is given by the p-value of Z when X = 1000 subtracted by the p-value of Z when X = 750, hence:
X = 1000:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1000 - 1500}{250}[/tex]
Z = -2
Z = -2 has a p-value of 0.0228.
X = 750:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{750 - 1500}{250}[/tex]
Z = -3
Z = -3 has a p-value of 0.0013.
0.0228 - 0.0013 = 0.0215.
0.02215 = 2.15% of bedroom apartments in the city cost between $750 and $1,000.
More can be learned about the normal distribution at https://brainly.com/question/24663213
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