QNT 351 Week 4 Problems

QNT
351 Week 4 Problems
1. Determine whether the random variable
is discrete or continuous.
a.
the number of textbook authors now sitting at a computer
b.
the weight of a T-bone steak
c.
the number of fish caught during a fishing tournament
d.
the time it takes to fly from city A to city B
e.
the number of points scored during a basketball game

2. Determine whether the random variable
is discrete or continuous. In each case, state the possible values of the
random variable.
(a)
the number of light bulbs that burn out in the next week in room with 17 bulbs
(b)
the amount of rain in City B during April

3. The random variable x has the following
discrete probability distribution. Complete parts a trough f.
a.
List the values x may assume.
b.
What value of x is most probable?
c.
Display the probability distribution as a graph. Choose the correct graph bellow.
d.
Find P(x=8)
e.
Find P(x?5)
f.
Find P(x>2)

4. A discrete random variable x can assume
five possible values 2, 3, 5, 7, and 9. Its probability distribution is shown
here. Complete parts a trough c.
a.
What is p(5)?
b.
What is the probability that x equals 2 or 9?
c.
What is p (x?7)?

5. Toss three fair coins and let x equal
the number of tails observed.
a.
Identify the sample points associated with this experiment and assign a value
of x to each sample point
b.
Calculate p(x) for the values x=1 and x=2
c.
Construct a graph for p(x)
d.
What is P(x=2 or x=3)?

6. Find the following probabilities for
the standard normal random variable z.
a.
P(z>1.79) b. P(z< -1.46) c. P(0.54 ? z ? 2.67) d. P(- 2.34 < z > 1.77)

7. Find the area under the standard normal
probability distribution between the following pairs of z – scores.
a.
z=0 and z=3.00
b.
z=0 and z=1.00
c.
z=0 and z=2.00
d.
z=0 and z=0.62

8. Find
the area under the standard normal probability distribution between the
following pairs of z – scores.
a.
z=0 and z=1.00
b.
z=0 and z=2.00
c.
z=0 and z=3.00
d.
z=0 and z=0.62

9. Find the following probability for the
standard normal random variable z.
P( –
1.5 ? z ? 1.5)

10. Suppose the random variable x is best
described by a normal distribution with µ = 26 and ? = 5. Find the z score that
corresponds to each of the following x – values.
a.
x=17 b. x=26 c. x=11
d. x=13 e. x=20 f. x=32

11. Suppose x is a normal distributed
random variable with µ = 11 and ? = 2. Find each of the following
probabilities.
a. P(x?14.5) b. P(x?9)
c. P(12.56?x?16.12) d.
P(5.84?x?13.42)

12. The ages of a group of 50 women are
approximately normally distributed with a mean of 48 years and a standard
deviation of 5 years. One woman is randomly selected from the group, and her
age is observed.
a.
Find the probability that her age will fall between 55 and 59 years.
b.
Find the probability that her age will fall between 47 and 53 years.
c.
Find the probability that her age will be less than 35 years.
d.
Find the probability that her age will exceed 41 years

13. Financial analysts who make forecasts
of stock prices are categorized as either “buy-side” analysts or “sell-side”
analysts. The mean and standard deviation of the forecast errors for both types
of analysts are shown is the table to the right. Assume that the distribution
of forecast errors are approximately normally distributed.
a.
Find the probability that a buy-side analyst has a forecast error of + 2.01 or
higher
b.
Find the probability that a sell-side analyst has a forecast error of + 2.01 or
higher

14. The mean gas mileage for a hybrid car
is 57 miles per gallon. Suppose that the gasoline mileage is approximately
normally distributed with a standard deviation of 3.5 miles per gallon.
a.
What is the probability that a randomly selected hybrid gets more than 62 miles
per gallon?
b.
What is the probability that a randomly selected hybrid gets 50 miles per gallon
or less?
c.
What is the probability that a randomly selected hybrid gets between 57 and 62
miles per gallon?
d.
What is the probability that a randomly selected hybrid gets less than 46 miles
per gallon?

15. Resource Reservation Protocol (RSVP)
was originally designed to establish signaling links for stationary networks.
RSVP was applied to mobile wireless technology. A simulation study revealed
that the transmission delay (measured is milliseconds) of an RSVP linked
wireless device has an approximate normal distribution with mean µ=46.5
milliseconds and ? = 8.5 milliseconds.
Complete
part a and b.