Question

The average weight of a house mouse is 0.68 ounces, with a standard deviation of 0.02 ounces. Assuming that the weight of house mice is normally distributed, what proportion of house mice weigh less than 0.67 ounces? (Select the answer that is closest to the answer that you calculated.)

a) -0.5

b) 0.309

c) 0.691

d) 0.5

e) 0.01

Answer 1

X ~ N ( µ = 0.68 , σ = 0.02 )
We convert this to standard normal as
P ( X < x ) = P ( Z < ( X - µ ) / σ )
P ( ( X < 0.67 ) = P ( Z < 0.67 - 0.68 ) / 0.02 )
= P ( Z < -0.5 )
P ( X < 0.67 ) = 0.309 (from Z table)