Respuesta :
The Solution:
Step 1:
We shall state the formula for calculating Z-score.
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ \text{Where X}=5\text{00 ( for lower limit) and X=550 for upper limit.} \\ \mu=400 \\ \sigma=50 \end{gathered}[/tex]Step 2:
We shall substitute the above values in the formula.
[tex]\begin{gathered} \frac{500-400}{50}\leq P(Z)\leq\frac{550-400}{50} \\ \\ \frac{100}{50}\leq P(Z)\leq\frac{150}{50} \\ \\ 2\leq P(Z)\leq3 \end{gathered}[/tex]Step 3:
We shall read the respective probabilities from the Z score distribution tables.
From the Z-score tables,
P(3) = 99.9 %
P(2) = 97.7 %
Step 4:
The Conclusion:
The probability that a worker selected makes between $500 and $550 is obtained as below:
[tex]\text{Prob}(500\leq Z\leq550)=99.9-97.7\text{ = 2.2 \%}[/tex]Therefore, the required probability is 2.2 %
