Question

Given that x is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that x is between 47 and 54.

Answer 1

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((x-mean)/(standard deviation) <(54 -50)/(2) )` -
`P((x-mean)/(standard deviation) <(47 -50)/(2) )`

= 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