Question

penelope loves to travel and sets aside a budget every year for her vacations. among her circle of friends, the average annual vacation budget is $3,000 with a standard deviation of $400. last year, penelope spent $3,500 on her vacations. what is penelopes last years vacation expenses z - score? use the following formula to calculate z - score: ( z=\frac{x - mu}{sigma} ) where ( x ) is the data point, ( mu ) is the mean, and ( sigma ) is the standard deviation.

Explanation:

Step1: Identify the values

Given \(x = 3500\), \(\mu=3000\), \(\sigma = 400\)

Step2: Substitute into the z - score formula

\(z=\frac{x - \mu}{\sigma}=\frac{3500 - 3000}{400}\)

Step3: Calculate the numerator

\(3500-3000 = 500\)

Step4: Calculate the z - score

\(z=\frac{500}{400}=1.25\)

Answer:

\(1.25\)