GeometryThe random variable x is normally distributed with mean mu=174
3 months ago
The random variable x is normally distributed with mean mu=174 and standard deviation sigma = 20 Find the indicated probability. P(x > 182)
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Best Answer
Czedowski Staff answered 3 months ago
Given: mu = 174 sigma = 20 We need to determine P(x>182). x=182 The z-score is the value x decreased by the mean and then divided by the standard deviation. z= (x- mu)/(sigma)= (182-174)/(20)= (8)/(20)= (2)/(5)=0.40 The probability to the left of z=0.40 is then given in the row with 0.4 and in the column with 0.00 of the standard normal table in the appendix. P(x<182)=P(z<0.40)=0.6554 Use the Complement rule: P(A^(c))=P(not A)=1-P(A) P(x>182)=1-P(x<182)=1-0.6554=0.3446 Result: 0.3446
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