Let X be the normal variable with mean μ =50 and standard deviation σ =2
We have to find probability that x is between 47 and 54
P(47 < X < 54) = P(X < 54) - P(X < 47)
= -
= P(Z < 2) - P(Z < -1.5)
Using standard normal z score table to find probabilities we get
P(Z < 2) = 0.9772
P(Z < -1.5) = 0.0668
P(47 < X < 54) = P(Z < 2) - P(Z < -1.5)
= 0.9772 - 0.0668
P(47 < X < 54) = 0.9104
The probability that x is between 47 and 54 is 0.9104