Question

the monthly expenses for a company are normally distributed with a mean of $5,000 and a standard deviation of $500. if the company had expenses of $5,750 in a particular month, what is the z - score for that months expenses? use the following formula to calculate z - score: z = (x - μ)/σ where x is the data point, μ is the mean, and σ is the standard deviation.

Explanation:

Step1: Identify values

$x = 5750$, $\mu=5000$, $\sigma = 500$

Step2: Substitute into z - score formula

$z=\frac{x - \mu}{\sigma}=\frac{5750 - 5000}{500}$

Step3: Calculate the numerator

$5750-5000 = 750$

Step4: Calculate the z - score

$z=\frac{750}{500}=1.5$

Answer:

1.5