SOLUTION: X is a normally distributed random variable with a mean of 7 and a standard deviation of 2.5. Find the value of X for which 70.54% of the area under the distribution curve lies to

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Question 1086122: X is a normally distributed random variable with a mean of 7 and a standard deviation of 2.5. Find the value of X for which 70.54% of the area under the distribution curve lies to the right of it. (Note: the diagram is not necessarily to scale.) (Hint: Find z corresponding to the given area and use X = z (standard deviation) + mean)
A. 6.10
B. 6.32
C. 5.65
D. 8.43
Answer by mathmate(429) About Me  (Show Source):
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Question:
X is a normally distributed random variable with a mean of 7 and a standard deviation of 2.5. Find the value of X for which 70.54% of the area under the distribution curve lies to the right of it. (Note: the diagram is not necessarily to scale.) (Hint: Find z corresponding to the given area and use X = z (standard deviation) + mean)

Solution:
mean=7
standard deviation=2.5
find X such that
P(z>Z)=.7054
P(z From normal distribution tables, Z=-0.54
Z=mean-0.54(standard deviation)=7-0.54*2.5=5.65