Question

A brisk walk at 4 miles per hour burns an average of 320 calories per hour. If the standard deviation of the distribution is 9 calories, find the probability that a person who walks 1 hour at the rate of 4 miles per hour will burn more 308 calories?

If necessary, round intermediate calculations to the nearest hundredth.

The probability that a randomly selected person burns more than 308 calories is ___%

Answer 1

Solution :

Given, X follows Normal distribution with,

   = 320

   = 9

Find P(X > 308)

= P[(X - )/ >  (308 - )/]

= P[Z > (308 - 320)/9]

= P[Z > -1.33]

= 1 - P[Z < -1.333]

= 1 - 0.0913 .......( use z table)

= 0.9087

P(X > 308) = 0.9087

The probability that a randomly selected person burns more than 308 calories is 90.87 %