Question

 A brisk walk at 4 miles per hour burns an average of 280 calories per hour. If the standard deviation of the distribution is 5 calories, find the probability that a person who walks 1 hour at the rate of 4 miles per hour will burn the given number of calories. Assume the random variable is normally distributed.

 Refer to the table of values (Area Under the Standard Normal Distribution ) as needed. If necessary, round intermediate calculations to the nearest hundredth.

 Part 1

 (a) More than 260 calories

 The probability that a randomly selected person burns more than 260 calories is _______ 

 Part 2

 (b) Less than 270 calories

 The probability that a randomly selected person burns less than 270 calories is _______ 

Answer 1

mean = 280 calories per hour

standard deviation = 5 calories

a)

more than 260 calories

finding z score

z score = ( x - mean ) / SD

= ( 260 - 280 ) / 5

finding probability using z score table

100 %

b)

less than 270 calories

z score = ( 270 - 280 )/ 5

2.28%

Answer 2

answer is 58.7%