For the general population the average number of miles walk

For the general population the average number of miles walk each day is 2.8 with a standard deviation of .64. What is the probability that a group of 16 people will walk a) At least 2 miles per day? b) No more than 2 miles a day? c) Between 1.5 and 2.9 miles per day.)

Solution

mean = u = 2.8
SD = 0.64
n = 16

a) Atleast 2 miles :

x = 2

z = (x - u) / (SD/sqrt(n))

z = (2 - 2.8) / (0.64 / sqrt(16))

z = -5

P(z > -5) = 1 ---> ANSWER

b) No more than 2 miles :

P(z < -5) = 0 ---> ANSWER

c)
Betwen 1.5 and 2.9

z = (1.5 - 2.8) / (0.64/sqrt(16))

z = -8.125

z = (2.9 - 2.8) / (0.64/sqrt(16))

z = 0.625

P(-8.125 < z < 0.625) to be found

0.734 ---> ANSWER