Statistics : At least 4 successes in 6 trials with p = 0.8

Subject: Mathematics    / Statistics
Question
1.
(1). At least 4 successes in 6 trials with p = 0.8
(2). At least 2 failures in 6 trials with p = 0.3
2.Text involving the computation of probabilities for a Bernoulli
trial. Assume that n = 10, and p =4/8.Find the probability of at
least 2 successes and at least 2 failures
3. Assume that the coin is weighted so that a tail is 4 times as
likely as a head. The coin is flipped 12 times.
What is the probability that both heads and tails occur
4. Assume that 8 questions are answered by guessing.What is the
probability of at least 6 correct answers
5. Good Vehicles, Inc., auto dealer, assume that 1 car in 8 is
defective and will not start.If at different times 4 individuals each
randomly select a car to test drive, what is the probability that at
least 1 of them selects a car that will not start
6. Assume that a box contains 3 defective widgets and 8
acceptable widgets. There are 4 inspectors, each of whom selects
a widget from the box at random, inspects it, and then replaces it
in the box. Each inspector makes his or her inspection at a
different time.
What is the probability that at least one inspector will find a
defective widget
7. Assume that 35 percent of voters are Republicans, 35 percent
are Democrats, and 30 percent are Independents. A poll taker
asks 8 people at random for their party affiliation. Assume further
that, because the city is so large, this situation can be
approximated by a Bernoulli process.
What is the probability that at least 5 of those polled are
Democrat voters?
8. professor who sometimes forgets to bring her briefcase to the
office, but assume that, each day, the probability that she forgets

the briefcase is
1/7. Assume that her forgetting is a Bernoulli process.
(1) What is the probability that she remembers to bring her
briefcase every day in one week (5 days)?
(2) What is the probability that she forgets to bring her briefcase
every day in one week (5 days)?
(3) What is the probability that she forgets to bring her briefcase
at least one day in one week (5 days)?
9. a basketball player’s three point shooting. Assume that his
shots are Bernoulli trials, and that he makes 2 in 8 of his shots.
How many three point shots must the player attempt so that the
probability of his hitting at least one of them is at least 0.99?
10. assume that the probability density function for the random
variable
Xis the one given in the table below:
Value of Probabili
X
ty
-4
0.2
0
0.3
1
0.1
5
0.4
What is the expected value of E[X]=
11. involving the expected value of a given probability density
function. Use the density function shown below instead of the one
in your text.
Value of Probabili
X
ty
6/16
-5
2/16
-3

2

3/16
3/16

4

2/16

-1

What is the expected value of this probability density function?
12. Assume that the drawer contains 14 coins: 5 quarters, 3
dimes, and 6 nickels. One coin is randomly selected.
What is the expected value of the coin selected (in cents)
13. simultaneous and random selection of three balls from a box,
but assume that the box contains 7 red balls and 5 blue balls. The
random variable,
Fill in the table below to complete the probability density function
of x,find the list values of x in ascending order
Value of X
0
1
2
3

Probability