Question

Given that X is a normally distributed variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54. There should be four decimal places in your answer.

Answer 1

We have find Probability P(47 < X < 54)

First lets convert this into standard normal form:

=> P( (47 - u)/s < (X - u)/s < (54 - u)/s)

where u = mean = 50 and s = standard deviation = 2

=> P( (47 - 50)/2 < (X - u)/s < (54 - 50)/2) and (X - u)/s = Z standard normally distributed Variable

=> P(-1.5 < Z < 2) = P(Z < 2) - P(Z < -1.5)

Using standard normal table we get:

P(-1.5 < Z < 2) = 0.9772 - 0.0668 = 0.9104

Hence, the probability that X is between 47 and 54 is 0.9104.