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. 

Answer 1

We have given that,

$\mu= 28$

$\sigma = 2$

We have to find the probability of its generating between 27 and 31 pounds of waste per month.

$P(27<X<31)$

$= P(\dfrac{27-28}{2}<Z<\dfrac{31-28}{2})$

$= P(-0.5<Z<1.5)$

$= P(0<Z<0.5)+P(0<Z<1.5)$

$= 0.19+0.43\\=0.62$