SOLUTION: Hi can someone please show me how to do questions like the following involving the normal probability distribution algebraically and using the inverse normal distribution formula (

Question 1117874: Hi can someone please show me how to do questions like the following involving the normal probability distribution algebraically and using the inverse normal distribution formula (z = X - mean/standard deviation)?
W is normally distributed with mean 1.5 and standard deviation 0.4. Z is the standard normal random variable. Find a if:
Pr(W < 0.5) = Pr(Z < a)
Pr(W < a) = Pr(Z > a/3)
Thankyou
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
W is normally distributed with mean 1.5 and standard deviation 0.4
:
Z is the standard normal random variable, this implies that the mean of Z is 0 and its standard deviation is 1
:
z-score(W) = (0.5 - 1.5)/0.4 = -2.5 and Pr(W<0.5) = 0.0062
:
z-score(Z) = (a - 0)/1 = -2.5 since Pr(W<0.5) = Pr(Z < a) and a = -2.5
:

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