Question

Research has indicated that the average distance women in rural Uganda walk to collect the day's water is 2.5 kilometers, with a standard deviation of 0.3 kilometers. Recently a study of women in the Masindi District of Uganda was conducted. What is the probability that a randomly selected woman walks more than 3 kilometers to collect the day's water, assuming the variable is normally distributed?

Answer 1

Let X be the random variable denoting the average distance that women in rural Uganda walk to collect day's water.

X is normally distributed with mean 2.5 kms and standard deviation 0.3 kms.

X~Normal(2.5,0.09)

ie. (X-2.5)/0.3~Normal(0,1)

To find the probability that a randomly selected woman walks more than 3 kms to collect day's water.

ie. to find P(X>3)

=P(X-2.5>3-2.5)

=P(X-2.5>0.5)

=P((X-2.5)/0.3>0.5/0.3)

=P(Z>1.66)

Where, Z is the standard normal variate.

=1-phi(1.66)

Where, phi is the distribution function of the standard normal variate.

=1-0.9515 (from the standard normal table)

=0.0485

Thus the required probability is 0.0485.