The probability that a selected worker makes $500 and $550 is 0.3413.
A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
[tex]x=\frac{x-\mu}{\sigma}[/tex]
Where,
z is standard score, or z score
x is observed value
μ is mean of the sample
σ is standard deviation of the sample
Converting a normal distribution into a z-distribution allows you to calculate the probability of certain values occurring and to compare different data sets.
According to the given question.
We have
[tex]x_{1} =400[/tex]
[tex]x_{2} = 450[/tex]
μ = 400
and, σ = 50
So,
[tex]z_{1} = \frac{x_{1}-\mu }{\sigma}[/tex]
[tex]\implies z_{1} = \frac{400-400}{50} =0[/tex]
and
[tex]z_{2} = \frac{x_{2}-\mu }{\sigma}[/tex]
[tex]\implies z_{2} = \frac{450-400}{50} = \frac{50}{50} = 1.00[/tex]
Therefore,
The probability that a selected worker makes $500 an d $550 is given by
[tex]P(0.00\leq z\leq 1.00)=0.3413-0.000=0.3413[/tex]
Hence, the probability that a selected worker makes $500 and $550 is 0.3413.
Find out more information about probability and z-score here:
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