Find probabilities using Normal Distribution

Question

Mean= 51 SD= 22 P(45 and 57)

(45-51)/22= -0.2727

(57-45)/22= 0.2727

Z chart 0.272= .9967

1-.9967= .0033

1-2(.0033)= 0.9934

I thought this was correct, but the answer is .215

Where did I make an error?

Answer 1

In the table I found on the internet, the table gives the area to the left of the Z score.

For the Z score of 0.2727, the area is approximately 0.606 to the left.

For the Z score of -0.2727, the area is approximately 0.394 to the left.

To find the area in between, subtract 0.606 -0.394 = 0.212 which is close to the correct answer.