Question

X is a normally distributed random variable with a mean of 8.0. Find the standard deviation of the distribution if 59.10% of the data lies to the right of 7.08. (Note: the diagram is not necessarily to scale.) How do I solve this with the calculator? Step by step please and thank you!

Answer 1

P(X < x) = P( Z < x - / )

We have to calculate such that

P( X > 7.08) = 0.5910

That is

P( Z > 7.08 - 8 / ) = 0.5910

P( Z < 7.08 - 8 / ) = 1 - 0.5910 = 0.4090

From Z table, z-score for the probability of 0.4090 is -0.2301

Therefore,

7.08 - 8 / = -0.2301

Solve for

= 3.9983 ( 4)