Question

convert each individual data value to a standardized z - score.
a - 1. ages of airline passengers: ( x = 85 ), ( mu = 49 ), ( sigma = 14 )
note: round your answer to 3 decimal places.
a - 2. is it an outlier?
no, this is an unusual observation.
no, this is not an outlier nor is it unusual.
yes, this is an outlier.
b - 1. fico credit scores: ( x = 579 ), ( mu = 711 ), ( sigma = 65 )
note: round your answer to 3 decimal places. negative amount should be indicated by a minus sign.
b - 2. is it an outlier?
no, this is an unusual observation.
no, this is not an outlier nor is it unusual.
yes, this is an outlier.
c - 1. condo rental vacancy days: ( x = 26 ), ( mu = 25 ), ( sigma = 6 )
note: round your answer to 3 decimal places.

Explanation:

Step1: Recall the z - score formula

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the data value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step2: Calculate the z - score for a - 1

For \(x = 85\), \(\mu=49\), \(\sigma = 14\), we substitute into the formula:
\(z=\frac{85 - 49}{14}=\frac{36}{14}\approx2.571\)

Step3: Determine if it is an outlier (a - 2)

A data point is considered an outlier if \(|z|>3\). Since \(|z| = 2.571<3\), but \(z>2\), it is an unusual observation.

Step4: Calculate the z - score for b - 1

For \(x = 579\), \(\mu = 711\), \(\sigma=65\), we substitute into the formula:
\(z=\frac{579 - 711}{65}=\frac{- 132}{65}\approx - 2.031\)

Step5: Determine if it is an outlier (b - 2)

Since \(|z|=2.031<3\) and \(|z|>2\), it is an unusual observation.

Step6: Calculate the z - score for c - 1

For \(x = 26\), \(\mu=25\), \(\sigma = 6\), we substitute into the formula:
\(z=\frac{26 - 25}{6}=\frac{1}{6}\approx0.167\)

Step7: Determine if it is an outlier (c - 2)

Since \(|z|=0.167<2\), it is not an outlier nor is it unusual.

Answer:

a - 1. \(z\approx2.571\)
a - 2. No, this is an unusual observation.
b - 1. \(z\approx - 2.031\)
b - 2. No, this is an unusual observation.
c - 1. \(z\approx0.167\)
c - 2. No, this is not an outlier nor is it unusual.