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Quiz 2
91.12.16
1. (30%)
Given that Z is a standard normal random variable and X is a normal
random variable with mean 4.5 and standard deviation 0.3..
(a)
P(2.5  Z  1.2)
(b)
P(1.24  Z  2.45)
(c)
P(1  Z  c)  0.68 . Find c.
(d)
P(4.8  X  5.04) .
(e)
P(c  X )  0.05 . Find c.
2. (30%)
(a) Let X be a continuous random variable with probability density
function
f ( x)  x 2 , 0  x  c
1

, c  x  12
.
12
 0, otherwise
Find c and mean of X.
(b) Let X be a Poisson random variable with the probability distribution
function
e q q i
P( X  i ) 
, i  0,1,2, .
i!
Show that
E( X )  q .
3. (30%)
Suppose the number of cars that arrive at a car wash is described by a
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Poisson distribution with a mean of 240 cars/per days.
(a) What is the probability that no car arrives within 2 hours?
(b) What is the probability that 5 cars arrive within 15 minutes?
(c) What is the probability that the time between the arrival is less than 30
miniutes?
4. (30%)
(a) A production process produces 90% non-defective parts. A sample
of 10 parts from the production process is selected. What is the
probability that the sample will contain no defective parts?
(b) A retailer of electronic equipment received 6 VCRs from the
manufacturer. 3 of the VCRs were damaged in the shipment. The retailer
sold 2 VCRs to 2 customers. What is the probability that one of the two
customers received a defective VCR?
(c) The length of time it takes students to complete a business statistics
examination is uniformly distributed and varies between 80 and 100
minutes. What is the variance for the amount of time it takes a student to
complete the examination?
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