1.
(a) P(X > 1) =>e^-1 = 0.367
(b) P(1 < X < 2.5)=
0.28579444254
(c) P(X = 3)=0
(d) P(X < 4)=
0.98168436111
(e) the value of a such that P(X ≥ a) = 0.10 : 2.3
2. The demand for water use in Phoenix in 2003 hit
a high of about 440 million gallons per day on June 27. Water use in the summer is normally
distributed with a mean of 320 million gallons per day and a standard deviation of 43 million gallons
per day. City reservoirs have a combined storage capacity of nearly 350 million gallons.
(a) What is the probability that a day requires more water than is stored in city reservoirs?
1-pnorm(350,320,43)= 0.2426904
(b) What reservoir capacity is needed so that the probability that it is exceeded is 1%? 219.967
qnorm(0.01,320,43)
(c) What amount of water use is exceeded with 95% probability? 390.7287
3. (Please provide necessary R statements) The number of views on a web site follows a Poisson
distribution with an average of 1.6 views per minute.
(a) What is the probability of no views in a minute? 1-pexp(1,1.6) = 0.2018965
(b) What is the probability of two or fewer views in 10 minutes?
(c) Determine the length of a time interval such that the probability of no views in an interval of
this length is 0.001. qexp(0.999,1.6)= 4.3
4.
a.