Answer:
The value that is greater than 45% of the data values is approximately 137.84.
Step-by-step explanation:
The key is transforming values from this distribution to a z-score range and finding the corresponding value using a z-score table.
We are looking for a value x which attains a critical z-score that corresponds to the (100-45)%=55-th percentile:
[tex]z_{0.55} = \frac{x-\mu}{\sigma}=\frac{x-140}{18}\implies x = 18\cdot z_{0.55}+140[/tex]
The critical z value (from z-score table, online) is: -0.12, so:
[tex]x = 18\cdot z_{0.55}+140=18\cdot(-0.12)+140\approx137.84[/tex]
The value that is greater than 45% of the data values is approximately 137.84.
Answer:
Formula for Z score
[tex]Z=\frac{X-B}{A}[/tex]
Where, Z is Z score for value that is greater than 45% of the data values.
X=Score=?
B=Mean =140
Standard Deviation = 18
Z score for value above 45 % of data set = 0.9987 - 0.0668=0.9319
[tex]Z_{45 percent above}=Z_{100}-Z_{45}=0.9987-0.0668=0.9319\\\\0.9319=\frac{X-140}{18}\\\\ 0.9319*18=X-140\\\\X=140 +16.7742\\\\ X=156.7742[/tex]
X score for value that is greater than 45% of the data values.= 156.78 (Approx)
