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Find the probability that her cats will wake her up no more than 5 times next week.

  • 0.5000
  • 0.9329
  • 0.0378
  • 0.0671

D: 0.0671

People visiting video rental stores often rent more than one DVD at a time. The probability distribution for DVD rentals per customer at Video To Go is given below. There is 5 video limit per customer at this store, so nobody ever rents more than 5 DVDs.

x 0 1 2 3 4 5
P(X=x) 0.03 0.50 0.24 ? 0.07 0.04
  • Describe the random variable X in words.
  • Find the probability that a customer rents three DVDs.
  • Find the probability that a customer rents at least 4 DVDs.
  • Find the probability that a customer rents at most 2 DVDs.

Another shop, Entertainment Headquarters, rents DVDs and videogames. The probability distribution for DVD rentals per customer at this shop is given below. They also have a 5 DVD limit per customer.

x 0 1 2 3 4 5
P(X=x) 0.35 0.25 0.20 0.10 0.05 0.05
  • At which store is the expected number of DVDs rented per customer higher?
  • If Video to Go estimates that they will have 300 customers next week, how many DVDs do they expect to rent next week? Answer in sentence form.
  • If Video to Go expects 300 customers next week and Entertainment HQ projects that they will have 420 customers, for which store is the expected number of DVD rentals for next week higher? Explain.
  • Which of the two video stores experiences more variation in the number of DVD rentals per customer? How do you know that?

Partial Answer:
A: X = the number of DVDs a Video to Go customer rents
B: 0.12
C: 0.11
D: 0.77

A game involves selecting a card from a deck of cards and tossing a coin. The deck has 52 cards and 12 cards are "face cards" (Jack, Queen, or King)The coin is a fair coin and is equally likely to land on Heads or Tails

  • If the card is a face card and the coin lands on Heads, you win $6
  • If the card is a face card and the coin lands on Tails, you win $2
  • If the card is not a face card, you lose $2, no matter what the coin shows.
  • Find the expected value for this game (expected net gain or loss).
  • Explain what your calculations indicate about your long-term average profits and losses on this game.
  • Should you play this game to win money?

The variable of interest is X = net gain or loss, in dollars

The face cards J, Q, K (Jack, Queen, King). There are(3)(4) = 12 face cards and 52 – 12 = 40 cards that are not face cards.

We first need to construct the probability distribution for X. We use the card and coin events to determine the probability for each outcome, but we use the monetary value of X to determine the expected value.

Card Event $X net gain or loss P(X)
Face Card and Heads 6 (12/52)(1/2) = 6/52
Face Card and Tails 2 (12/52)(1/2) = 6/52
(Not Face Card) and (H or T) –2 (40/52)(1) = 40/52
  • Expected value = (6)(6/52) + (2)(6/52) + (–2) (40/52) = –32/52
  • Expected value = –$0.62, rounded to the nearest cent
  • If you play this game repeatedly, over a long number of games, you would expect to lost 62 cents per game, on average.
  • You should not play this game to win money because the expected value indicates an expected average loss.

You buy a lottery ticket to a lottery that costs $10 per ticket. There are only 100 tickets available be sold in this lottery. In this lottery there is one $500 prize, 2 $100 prizes and 4 $25 prizes. Find your expected gain or loss.

Start by writing the probability distribution. X is net gain or loss = prize (if any) less $10 cost of ticket

X = $ net gain or loss P(X)
$500–$10=$490 1/100
$100–$10=$90 2/100
$25–$10=$15 4/100
$0–$10=$–10 93/100)

Expected Value = (490)(1/100) + (90)(2/100) + (15)(4/100) + (–10) (93/100) = –$2.There is an expected loss of $2 per ticket, on average.

A student takes a 10 question true-false quiz, but did not study and randomly guesses each answer. Find the probability that the student passes the quiz with a grade of at least 70% of the questions correct.

  • X = number of questions answered correctly
  • X~B(10, 0.5)
  • We are interested in AT LEAST 70% of 10 questions correct. 70% of 10 is 7. We want to find the probability that X is greater than or equal to 7. The event "at least 7" is the complement of "less than or equal to 6".
  • Using your calculator's distribution menu: 1 – binomcdf(10, .5, 6) gives 0.171875
  • The probability of getting at least 70% of the 10 questions correct when randomly guessing is approximately 0.172

A student takes a 32 question multiple choice exam, but did not study and randomly guesses each answer. Each question has 3 possible choices for the answer. Find the probability that the student guesses more than 75% of the questions correctly.

  • X = number of questions answered correctly
  • X~B(32, 1/3)
  • We are interested in MORE THAN 75% of 32 questions correct. 75% of 32 is 24. We want to find P(x>24). The event "more than 24" is the complement of "less than or equal to 24".
  • Using your calculator's distribution menu: 1 - binomcdf(32, 1/3, 24)
  • P(x>24) = 0.00000026761
  • The probability of getting more than 75% of the 32 questions correct when randomly guessing is very small and practically zero.

Suppose that you are perfoming the probability experiment of rolling one fair six-sided die. Let F be the event of rolling a "4" or a "5". You are interested in how many times you need to roll the die in order to obtain the first “4 or 5” as the outcome.

  • p = probability of success (event F occurs)
  • q = probability of failure (event F does not occur)
  • Write the description of the random variable X. What are the values that X can take on? Find the values of p and q.
  • Find the probability that the first occurrence of event F (rolling a “4” or “5”) is on the second trial.
  • How many trials would you expect until you roll a “4” or “5”?

A: X can take on the values 1, 2, 3, .... p = 2/6, q = 4/6
B: 0.2222
C: 3

**Exercises 38 - 43 contributed by Roberta Bloom

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Collaborative statistics (custom lecture version modified by t. short). OpenStax CNX. Jul 15, 2013 Download for free at http://cnx.org/content/col11543/1.1
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