find the area under the curve N(100,15) from x=95 to x=115

Question

it just saids font the area under the curve N9100,) from x=95 to x=115

Answer 1

I guess N(100,15) implies a normal distribution where 100 is the mean and SD=15. The z scores for 95 and 115 are (95-100)/15=-0.3333 and (115-100)/15=1.0000. The values from the table are 0.3694 and 0.8413 respectively. The difference gives the area under the distribution curve=0.4719, because the table gives cumulative probabilities equivalent to areas under the curve.