Respuesta :
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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
A salary of $510.10 has a z-score of -0.50.
Putting values, we get,
[tex]-0.50 = \displaystyle\frac{510.10-\mu}{145.80}\\\\\mu = 0.50(145.80) + 510.10\\\Rightarrow \mu = 583[/tex]
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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
The salary of $2,291.90 has a z-score of +0.50
Putting values, we get,
[tex]0.50 = \displaystyle\frac{2291.90-2132}{\sigma}\\\\\sigma= \frac{2291.90-2132}{0.50}\\\\\sigma = 319.8[/tex]
Thus, the standard deviation of the salary of firefighters in Portugal is $319.8
