Question

1. Each month, the city of Accra generates an average of 28 pounds of waste. Assume the variable is approximately normally distributed and the standard deviation is 2 pounds. If a household is selected at random, find the probability of its generating between 27 and 31 pounds of waste per month. Draw a normal distribution curve to show the required region.
2. It is assumed that consumption C depends on income Y and that this relationship takes the form of the linear function C = a + bY. When Y is GH¢600, C is observed to be GH¢660. When Y is 1,000, C is observed to be GH¢900. What are the values of a and b in this function? Express C in terms of Y only. Find the consumption if a family’s income is GH¢1,200.

Answer 1

1. Answer: given: an average of 28 pounds

a.

Find z values corresponding to 27 and 31:

z=%2827-28%29%2F2=-1%2F2=-0.5

z=%2831-28%29%2F2=3%2F2=1.5

Find the area between z+=+-0.5 and z=+1.5

Table E gives us an area of 0.9332-0.30=0.6247=> The probability is 62.47%

b.

Find z values corresponding to 30.2

z=%2830.2-28%29%2F2=2.2%2F2=1.1 Find the area to the right of z+=1.1

it gives you an area of 0.1357=> The probability is 13.57%