Answer to Question #197320 in Statistics and Probability for Dadzie Mustapha

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.

$P(27<X<31)$

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

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

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

$= 0.19+0.43\\=0.62$