Question

Let X be normally distributed with the mean μ = 100 and some unknown standard deviation σ. The variable Z = X − A σ is distributed according to the standard normal distribution. Enter the value for A =  . It is known that P ( 95 < X < 105 ) = 0.5. What is P ( − 5 σ < Z < 5 σ ) =  (enter decimal value). What is P ( Z < 5 σ ) =  (as a decimal). Use this result to determine σ =  (round to the third decimal place).

Answer 1

X is normally distributed   

Z is standard normal random variable. So,   

According to the given question, I have got the above values. But it does not satisfy  P ( 95 < X < 105 ) = 0.5.

So, is the question correct? Should it be ??? or something else????

Please comment.