The random variable x is normally distributed with mean
mu=174
and standard deviation
sigma = 20
Find the indicated probability. P(x > 182)

1 Answers

Best Answer

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