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Answer:
That is, 60% of the values are greater than 188.25
244.18 is below 17% of the values
22% of the values are less than 163.81
205.64 is greater than 55% of the values
step-by-step explanation:
Use the standard normal distribution table attached.
- 60% of the values are greater than x is equivalent to find Z = 40% = 0.4 (that is, the right tail has 60% of the area in it). In this case:
Z = -0.25
Z is computed as follows:
Z = (x - mean)/standard deviation
Replacing:
-0.25 = (x - 200)/47
x = -0.25*47 + 200 = 188.25
- x is below 17% of the values. That is equivalent to: right-tail has 17% of the area. To get this, find Z which are is 0.17 and multiply it by -1, then, solve to find x:
Z = -0.94
0.94 = (x - 200)/47
x = 0.94*47 + 200 = 244.18
- 22% of the values are less than x. That is equivalent to: left tail of 22%. From the figure we see that correspond to Z = -0.77. Therefore:
-0.77 = (x - 200)/47
x = -0.77*47 + 200 = 163.81
- x is greater than 55% of the values. That is equivalent to: left tail of 55%. To get this, find Z with 45% in the table, which is -0.12, multiply it by -1, which makes Z = 0.12. Then:
0.12 = (x - 200)/47
x = 0.12*47 + 200 = 205.64
