SOLUTION: X is a normally distributed random variable with a mean of 10.00. If the probability that X is less than 11.54 is 0.67 (as shown below), then what is the standard deviation of X?

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Question 962665: X is a normally distributed random variable with a mean of 10.00. If the probability that X is less than 11.54 is 0.67 (as shown below), then what is the standard deviation of X? Round to 2 decimal places.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
P(Z < z) = 0.67 has the solution z = 0.4399

So P(Z < 0.4399) = 0.67 approximately

You use a calculator or table to determine this.

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z = (x-mu)/sigma

0.4399 = (11.54-10)/sigma

0.4399 = 1.54/sigma

0.4399*sigma = 1.54

sigma = 1.54/0.4399

sigma = 3.5007956

sigma = 3.50

The standard deviation is approximtely 3.50

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