Normal distribution

Question

A brisk walk at 5 miles per hour burns an average of 320 calories per hour. If the standard deviation of the distribution is 8 calories/hour, find the percentage of people who walk at 5 miles per hour for 1 hour that will burn off between 290 and 340 calories

Answer 1

x = calories N(320,5)

P(290 < x < 340)

convert above inequality to z score N(0,1)

z = (x - mean)/SD = (x - 320)/8

P(290 < x < 340) = P((290-320)/8 < z < (340-320)/8) = P( -3.75 < z < 2.5) = P(z < 2.5) - P(z < -3.75) = 0.9938