Question

Relationships between means, standard deviations, X values,and z-scores

Answer 1

Answer:

a) The average salary of firefighters in Portugal is $583.

b) The standard deviation of the salary of firefighters in Portugal is $319.8

Step-by-step explanation:

We are given the following in the question:

a) Standard Deviation, σ = $145.80

We are given that the distribution of salary of professor is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

A salary of $510.10 has a z-score of -0.50.

Putting values, we get,

$-0.50 = \displaystyle\frac{510.10-\mu}{145.80}\\\\\mu = 0.50(145.80) + 510.10\\\Rightarrow \mu = 583$

Thus, the average salary of firefighters in Portugal is $583.

b) Mean, μ = $2,132

We are given that the distribution of salary of computer programmers is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

The salary of $2,291.90 has a z-score of +0.50

Putting values, we get,

$0.50 = \displaystyle\frac{2291.90-2132}{\sigma}\\\\\sigma= \frac{2291.90-2132}{0.50}\\\\\sigma = 319.8$

Thus, the standard deviation of the salary of firefighters in Portugal is $319.8