Question

Each month, an American household generates an average of 28 pounds of newspaper for garbage and/or recycling. Assume this is approximately normally distributed and that the standard deviation is 2 pounds. If a household is selected at random, find the probability of it generating between 27–31 pounds per month.

Answer 1

Solution:

We are given

µ = 28

σ = 2

We have to find P(27<X<31)

P(27<X<31) = P(X<31) - P(X<27)

Find P(X<31)

Z = (X - µ)/σ

Z = (31 - 28)/2

Z = 1.5

P(Z<1.5) = P(X<31) = 0.933193

(by using z-table)

Now find P(X<27)

Z = (X - µ)/σ

Z = (27 - 28)/2

Z = -0.5

P(Z<-0.5) = P(X<27) = 0.308538

(by using z-table)

P(27<X<31) = P(X<31) - P(X<27)

P(27<X<31) = 0.933193 - 0.308538

P(27<X<31) = 0.624655

Required probability = 0.624655