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Sagot :
ANSWER :
The answers are :
a. 3.03
b. -9.09
c. 55.775 lbs
EXPLANATION :
The z-score formula is :
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \text{ where :} \\ \text{ x = sample weight} \\ \mu\text{ = mean weight} \\ \sigma\text{ = standard deviation} \end{gathered}[/tex]From the problem, we have :
[tex]\mu=50\text{ }lbs\quad and\quad\sigma=3.3\text{ }lbs[/tex]a. z-score when x = 60 lbs.
That will be :
[tex]\begin{gathered} z=\frac{60-50}{3.3} \\ z=3.03 \end{gathered}[/tex]b. z-score when x = 30 lbs below the mean, the mean weight is 50 lbs, so it will be x = 50 - 30 = 20
The z-score will be :
[tex]\begin{gathered} z=\frac{20-50}{3.3} \\ z=-9.09 \end{gathered}[/tex]c. weight when it is 1.75 standard deviations above the mean weight.
Above the mean weight denotes that the z-score is positive.
Substitute z = 1.75 and solve for x :
[tex]\begin{gathered} 1.75=\frac{x-50}{3.3} \\ 1.75(3.3)=x-50 \\ x=1.75(3.3)+50 \\ x=55.775 \end{gathered}[/tex]
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