Question

X is a normally distributed random variable with a mean of 4.0. Find the standard deviation of the distribution if 59.10% of the data lies to the right of 3.54. (Note: the diagram is not necessarily to scale.) Group of answer choices

A. 1.0

B. 2.0

C. 0.5

D. 1.3

Answer 1

Mean, = 4.0

Standard deviation =

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

P(X > 3.54) = 0.5910

P(X < 3.54) = 1 - 0.5910 = 0.4090

P(Z < (3.54 - 4)/) = 0.4090

Take the value of Z corresponding to 0.4090 from standard normal distribution table

(3.54 - 4)/ = -0.23

-0.46/ = -0.23

= 2