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The formula for Z-Score is: (x-mu)/sigma. We know from the information given that Z=0.5, mu=300 & sigma=100. Solve for x and plug in the values. X=Z*sigma+mu; x=0.5*100+300 or x=350. So, $350 is amount spent on books.
Z-score is the x value minus the mean, all divided by the standard deviation; or z=(x-mu)/sigma. The "x" value needs to be given to answer the question.
The z-score can't be calculated with the information given. A mean & standard deviation is required to put into the formula: Z = (x-mean)/sigma. Your x value is 10.
There are three sigma symbols, an upper case, a lower case and an end of the sentence case. The capital letter case is used as summation. The lower case is used to represent variance in statistics. The lower case is also used to represent stress in mechanics and physics. The end of sentence case is generally not used. Reference link: http://en.wikipedia.org/wiki/Sigma.
formula for finding mean through direct mean method: sigma fi xi /sigma fi