Once an individual has been infected with a certain disease, letXrepresent the time (days) that elapses before the individual becomes infectious. An article proposes a Weibull distribution with

=2.3,

=1.5,

and

= 0.5.

[Hint: The two-parameter Weibull distribution can be generalized by introducing a third parameter, called athresholdorlocationparameter: replacexin the equation below,

f(x;,) =

x1e(x/)		x0
0		x< 0

by x and x0 by x.]

(a)Calculate

P(1 <X< 2).

(Round your answer to four decimal places.)

(b)Calculate

P(X> 1.5).

(Round your answer to four decimal places.)

(c)What is the 90th percentile of the distribution? (Round your answer to three decimal places.) ______days

(d)What are the mean and standard deviation ofX? (Round your answers to three decimal places.)

mean_____ days

standard deviation_______ days