**Answer:**

**(a) Between 27 and 31 pounds per month = 0.62465**

**(b) More than 30.2 pounds per month = 0.1357**

**Step-by-step explanation:**

We are given that each month, an American household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the standard deviation is 2 pounds and the variable is approximately normally distributed.

<em>Let X = generation of newspaper for garbage or recycling</em>

**The z-score probability distribution for normal distribution is given by;**

Z = ~ N(0,1)

where, = population average = 28 pounds

= population standard deviation = 2 pounds

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

(a) **Probability of household generating between 27 and 31 pounds per month is given by = P(27 pounds < X < 31 pounds) = P(X < 31 pounds) - P(X **** 27 pounds)**

P(X < 31 pounds) = P( < ) = P(Z < 1.50) = 0.93319

P(X 27 pounds) = P( ) = P(Z -0.50) = 1 - P(Z < 0.50)

= 1 - 0.69146 = 0.30854

<em>{Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.50 and x = 0.50 in the z table which has an area of 0.93319 and 0.30854 respectively.}</em>

**Therefore, P(27 pounds < X < 31 pounds) = 0.93319 - 0.30854 = 0.62465**

(b) **Probability of household generating more than 30.2 pounds per month is given by = P(X > 30.2 pounds)**

** **P(X > 30.2 pounds) = P( > ) = P(Z > 1.10) = 1 - P(Z <em>** **</em>1.10)

= 1 - 0.8643 = 0.1357

<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.10 in the z table which has an area of 0.8643.</em>** **