Question

A weather forecaster predicts that the rainfall in November in a local area will be between two and eight inches but has no idea where within the interval the actual amount will be. In other words, all amounts within that interval are equally likely.

(b) What would be a reasonable probability distribution to use to model the rainfall--assuming that the likelihood of rain over the range of possible amounts is the same?  

(c) X ~  (  ,  )

(d) Write the formula for the probability density function of X.

pdf(x) = /   for   < x <   

(e) What is the probability that rainfall will be at most six inches?  

P(X ≤ 6 ) =

(f) What is the probability that rainfall will be more than six inches?

P(X > 6 ) =

Answer 1

(b)

A reasonable probability distribution to use to model the rainfall--assuming that the likelihood of rain over the range of possible amounts is the same:

Uniform Distribution defined in the interval [2,8]

(c)

(d)

Probability Density Function of X is given by:

                          for 2 X 8

     = 0,   otherwise

(e)

So,

Answer is:

0.6667

(f)

So,

Answer is:

0.3333