The average teacher's salary in a particular state is $54,148. If the standard deviation is $10,210 , find the salaries according to the z-score, z=3

Question

The average teacher's salary in a particular state is $54,148. If the standard deviation is $10,210 , find the salaries according to the z-score, z=3

Answer 1

the underlying formula that you want to use here is

Z = (x - mean) / (standard deviation)

for this scenario that means taking

3 = (x - 54148) / 10210

x = 3(10210) + 54148

x = 84778

meaning that the teacher's salary corresponding to a Z-score of 3 is $84,778

Answer 2

Recall the definition of z-score of a value in a distribution is: z = (x-µ)/σ, where x is the observed value, µ is the mean, and σ is the standard deviation.

You have three of the values provided already. Plug these values in and solve the equation for x.

Answer 3

The average teacher's salary in a particular state is $54,148. If the standard deviation is $10,210 , find the salaries according to the z-score, z=3

z = (x - xbar) / sd

3 = (x - 54148) / 10210

x - 54148 = 3 * 10210 = 30630

x = 30630 + 54148 = 84778.

Hence, the salaries is $84,778