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 $1,000 with a standard deviation of $400. last year, penelope spent $1,500 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: Substitute values into formula

Given \(x = 1500\), \(\mu=1000\), \(\sigma = 400\). Use \(z=\frac{x - \mu}{\sigma}\).

$$z=\frac{1500 - 1000}{400}$$

Step2: Calculate the numerator

\(1500-1000 = 500\). So \(z=\frac{500}{400}\)

Step3: Simplify the fraction

\(\frac{500}{400}=\frac{5}{4}=1.25\)

Answer:

1.25