Question

1. Organizers of a concert are limiting ticket sales to a maximum of 4 tickets per customer. Past experience has shown that the probability distribution of the number of tickets purchased in these situations is:

Number of Tickets Purchased | Probability |

1 | 0.1 |

2 | 0.3 |

3 | 0.2 |

4 | 0.4 |

What is the expected value of the number of tickets purchased? Include 1 decimal place in your answer.

2.

Kelsie works at a bicycle shop as a salesperson. The probability distribution of the number of bicycles Kelsie sells on a randomly selected day is shown below:

Number of Bicycles Sold | Probability |

0 | 0.30 |

1 | 0.50 |

2 | 0.15 |

3 | 0.05 |

The mean for the number of bicycles sold is 0.95. What is the standard deviation? Round your answer to 2 decimal places.

Answer #1

1)

x | P(x) | x * P(x) |

1 | 0.1 | 0.1 |

2 | 0.3 | 0.6 |

3 | 0.2 | 0.6 |

4 | 0.4 | 1.6 |

Sum | 1 | 2.9 |

Mean = = X * P(X) = 2.9

the expected value of the number of tickets purchased = 2.9

2)

x | P(x) | x * P(x) |
x^{2} * P(x) |

0 | 0.3 | 0 | 0 |

1 | 0.5 | 0.5 | 0.5 |

2 | 0.15 | 0.3 | 0.6 |

3 | 0.05 | 0.15 | 0.45 |

Sum | 1 | 0.95 | 1.55 |

Mean = = X * P(X) = 0.95

Standard deviation =

=X
^{2} * P(X) -
^{2}

= 1.55
- 0.95^{2}

**= 0.80**

For an upcoming concert, each customer may purchase up to 3
child tickets and 3 adult tickets. Let C be the number of child
tickets purchased by a single customer. The probability
distribution of the number of child tickets purchased by a single
customer is given in the table below.
c
0
1
2
3
p(c)
0.4
0.3
0.2
0.1
a) Compute mean and standard deviation of C.
b) Suppose the mean and standard deviation for the number of
adult...

A senior citizen purchases 45 lottery tickets a week,
where each ticket consists of a different six-number combination.
The probability that this senior will win - (to win at least three
of the six numbers on the ticket must match the six-number winning
combination) on any ticket is about 0.018638.
What probability distribution would be appropriate for
finding the probability of any individual ticket
winning?
Binomial, Negative Binomial, Hypergeometric, or
Poisson?
1. How many winning tickets can the senior expect...

1) A raffle offers one $1000.00 prize, one $500.00 prize, and
five $200.00 prizes. There are 5000 tickets sold at $4 each. Find
the expectation if a person buys one ticket.
2) The number of cartoons watched on Saturday mornings by
students in Mrs. Kelly's first grade class is shown below.
Number of cartoons watched
X
0
1
2
3
4
5
Probability P(X)
0.15
0.20
0.30
0.10
0.20
0.05
Give the standard deviation for the probability distribution.

Tickets for a raffle cosr $$8. There were 842 tickets sold. One
ticket will be randomly selected as the winner, and that person
wins $$1900 and also the person is given back the cost of the
ticket. For someone who buys a ticket, what is the Expected Value
(the mean of the distribution)?
If the Expected Value is negative, be sure to include the "-" sign
with the answer. Express the answer rounded to two decimal
places.
Expected Value =...

1. You are considering buying a raffle ticket for $10. One
thousand tickets are being sold and the winner gets $6,000. The
winning number will be randomly drawn, so your probability of
winning is .001 (=0.1%). If you win, the net benefit to you is
$5,990 (the $6,000 winnings minus the $10 you paid for the ticket).
If you lose, the net benefit is minus $10 (the cost of the
ticket).
2. Your car insurance company has learned, from years...

1. Every 5th ticket in a raffle wins a prize. Jim
buys 4 tickets. What is the probability that he wins at least one
prize?
2. Two dice are rolled 4 times. Find the probability that
exactly two times the sum of the outcomes will be greater than
9.
3. Larry is driving from Boston, MA, to Hartford, CT, and he is
speeding. The fines for speeding are $200 in CT and $150 in MA, and
the probabilities of getting...

1. Suppose the value of a stock varies each day from $16 to $25
with a uniform distribution. Find s.
Group of answer choices
A. 20.5
B. 11.8
C. 17
D. 2.6
2. Find the mean of the probability distribution:
x P(x)
2 0.33
3 0.24
4 0.43
Group of answer choices
A. 2.60
B. 3.10
C. 1.60
D. 2.10
3. The number of cartoons watched by Mrs. Kelly's first grade
class on Saturday morning is shown below:
x...

Consider the probability distribution shown below.
x
0
1
2
P(x)
0.05
0.50
0.45
Compute the expected value of the distribution.
Consider a binomial experiment with
n = 7 trials
where the probability of success on a single trial is
p = 0.10.
(Round your answers to three decimal places.)
(a) Find
P(r = 0).
(b) Find
P(r ≥ 1)
by using the complement rule.
Compute the standard deviation of the distribution. (Round your
answer to four decimal places.)
A...

Question 2
Given the following probability distribution, what is the
expected value?
Outcome
P(Outcome)
20
0.15
1
0.15
19
0.10
2
0.09
17
0.51
Round to 3 decimal places as needed.
Question 3
Brandybuck Insurance Company (BIC) is deciding whether to insure
the lives of those leading a quest to Moria. Based on past
experience, the probability of surviving such a quest is 83.4%. If
BIC charges a premium of 8,565 silver coins and would pay a death
benefit of...

1.A fair die is rolled once, and the number score is noted.
Let the random variable X be twice this score. Define the variable
Y to be zero if an odd number appears and X otherwise. By finding
the probability mass function in each case, find the expectation of
the following random variables:
Please answer to 3 decimal places.
Part a)X
Part b)Y
Part c)X+Y
Part d)XY
——-
2.To examine the effectiveness of its four annual advertising
promotions, a mail...

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