Bob and John are traveling from city A to city D. Bob decides

Q1 ) Bob and John are traveling from city A to city D. Bob decides
to take the upper route (through B) whereas John takes the lower
route (though C) as shown in the following figure:
The travel times (in hours) between the cities indicated are
normally distributed as follows:
T1 ~ N(6,4),T2 ~ N(4,1),T3 ~ N(5,9),T4 ~ N(4,1)
The travel times for T1 and T2 are independent, but T3 and T4 are
dependent with covariance 2.4.
a) Which route (upper or lower) should be taken if one wishes to
minimize the expected travel time from A to D? Justify
.  b) What is the probability that Bob will not arrive in city D
within ten hours?  ?
.  c) What is the probability that John will not arrive in city D
within ten hours?  ?
d) What is the probability that Bob will arrive earlier than John?
Q2) A survey was recently done and it was found that of the 120
households who were randomly contacted, 20 of them did not own
a television set. Based on this information our estimate of the
proportion of household’s without a television is 0.1667.
The New York Post uses the survey data to make the claim that
less than 20% of American households don’t own a television set.
The New York Times uses the same survey data to make the claim
that less than 25% of American households don’t own a television
set. Which claim is supported more by the observed evidence?
Justify. [hint we want you to compare Ho : p = .2 Ha : p < .2 and
Ho: p =.25 Ha: p <.25]
Q3) Let  be some number between 0 and 1 and define the
following discrete probability distribution for the random variable
X:
a) Show that this is a legal probability distribution.
b) We want to estimate based on one observation. Suppose we
define our estimator to be
Show that this is an unbiased estimator of .
Q4) A 95% confidence interval for a population proportion
calculated using data from a random sample of size n = 500
is (0.13, 0.73). Which of the following is the margin of error
of this interval?
?
Q5) When two Labrador retrievers breed, theory says there
should be 50% black, 40% yellow and 10% chocolate
offspring. Two Labrador retrievers are bred and a litter
consisting of 3 black dogs, 5 yellow dogs, and 2 chocolate
dogs is produced. For a goodness of fit test, the  statistic
would be:  ?