Question

A brisk walk at 4 mph burns an average of 300 calories per hour. If the standard deviation is 8 calories per hour, what is the probability that someone who walks one hour will burn between 285 and 320 calories?

z-score for 285 calories

table value for this z-score

z-score for 320 calories

table value for this z-score

final answer

summary statement

Answer 1

Solution :

mean = = 300

standard deviation = = 6

a ) P ( 285 < x < 331 )

P ( 285 - 300 / 8) < ( x -  / ) < ( 320 - 300 / 8)

P ( - 15 / 8 < z < 20 / 8 )

P (-1.87 < z < 2.5)

P ( z < 2.5 ) - P ( z < -1.87)

Using z table

= 0.9938 - 0.0307

= 0.9631

Probability = 0.9631

b ) x =  285

Using z-score formula,

z = x -  /

= 285 - 300 / 8

= -15 /8

z = -1.87

c) x =  320

Using z-score formula,

z = x -  /

= 3520 - 300 / 8

= 20 /8

z = 2.50