The following density function describes a random variable X. f(x)= (x/64) if 0<x<8 and f(x) = (16-x)/64 if 8<x<16
A. Find the probability that X lies between 2 and 6.
B. Find the probability that X lies between 5 and 12.
C. Find the probability that X is less than 11.
D. Find the probability that X is greater than 4.
In: Statistics and Probability
What’s the probability of getting no heads after flipping a fair coin 10 times? What’s the probability of getting no 3’s after rolling a fair 6-sided die 9 times? What’s the probability of getting a 4 at least once after rolling a fair 4-sided die 5 times? What’s the probability of getting a 5 exactly once after rolling a fair 8-sided die 7 times?
In: Math
In 2008, the per capita consumption of soft drinks in Country A was reported to be 18.15 gallons. Assume that the per capita consumption of soft drinks in Country A is approximately normally distributed, with a mean of 18.15 gallons and a standard deviation of 5 gallons. Complete parts (a) through (d) below
. a. What is the probability that someone in Country A consumed more than 10 gallons of soft drinks in 2008? The probability is nothing. (Round to four decimal places as needed.)
b. What is the probability that someone in Country A consumed between 3 and 6 gallons of soft drinks in 2008? The probability is nothing. (Round to four decimal places as needed.)
c. What is the probability that someone in Country A consumed less than 6 gallons of soft drinks in 2008? The probability is nothing. (Round to four decimal places as needed.)
d. 97% of the people in Country A consumed less than how many gallons of soft drinks? The probability is 97% that someone in Country A consumed less than select: ___ gallons of soft drinks. (Round to two decimal places as needed.)
In: Statistics and Probability
A study conducted by a research group in a recent year reported that 58% of cell phone owners used their phones inside a store for guidance on purchasing decisions. A sample of 16 cell phone owners is studied. Round the answers to at least four decimal places.
A) What is the probability that seven or more of them used their phones for guidance on purchasing decisions? The probability that seven or more of them used their phones for guidance on purchasing decisions is...?
B) What is the probability that fewer than eight of them used their phones for guidance on purchasing decisions? The probability that fewer than eight of them used their phones for guidance on purchasing decisions is...?
C) What is the probability that exactly nine of them used their phones for guidance on purchasing decisions? The probability that exactly nine of them used their phones for guidance on purchasing decisions is...?
D) Would it be unusual if more than 11 of them used their phones for guidance on purchasing decisions? It would/would not be unusual if more than 11 of them used their phones for guidance on purchasing decisions since the probability is ...?
In: Statistics and Probability
What college basketball conferences have the higher probability of having a team play in college basketball's national championship game? Over the last 20 years, Conference A ranks first by having a team in the championship game 11 times. Conference B ranks second by having a team in the championship game 8 times. However, these two conferences have both had teams in the championship game only one time. Use these data to estimate the following probabilities.
(a)
What is the probability that Conference A will have a team in the championship game?
(b)
What is the probability that Conference B will have a team in the championship game?
(c)
What is the probability that Conference A and Conference B will both have teams in the championship game?
(d)
What is the probability at least one team from these two conferences will be in the championship game? That is, what is the probability a team from Conference A or Conference B will play in the championship game?
(e)
What is the probability that the championship game will not a have team from one of these two conferences?
In: Statistics and Probability
Shortly before midnight, on April 14, 1912, the Titanic collided with an iceberg and sank.
Out of the 2249 passengers, 1514 died that night. The passengers’ summarized data are shown below:
| 1st Class | 2nd Class | 3rd Class | Crew | Total | |
| Survived | 209 | 125 | 183 | 218 | 735 |
| Died | 127 | 174 | 536 | 677 | 1514 |
| 336 | 299 | 719 | 895 | 2249 |
(Round all answers to four decimals)
Suppose a passenger is selected at random:
a) What is the probability that the passenger survived?
b) What is the probability that the passenger was in 3rd class?
c) What is the probability that the passenger survived and was a crew member?
d) What is the probability that the passenger was not in 1st class?
e) “Surviving” is (Click to select) dependent disjoint independent mutually exclusive of “being in 1st class”.
f) Suppose the passenger selected was in 2nd class. What is the probability that the passenger died?
g) What is the probability that a surviving passenger was a crew member?
h) What is the probability that the passenger survived or was a crew member?
i) “Surviving” and “being in 3rd class” are
In: Statistics and Probability
Use this table to answer the following questions.
| # of siblings | 0-2 | 3-5 | 6 or more | Total |
| Broncos Fan | 8 | 9 | 16 | 33 |
| Not a Broncos Fan | 1 | 7 | 4 | 12 |
| Total | 9 | 16 | 20 | 45 |
a) If a random a person was selected, what would be the
probability that the person was not a Broncos fan ?
b) Given that a person is a Broncos fan, what is the probability
that they have 6 or more siblings?
c) Given that a person has 3-5 siblings, what is the probability
that the person is not a Broncos fan?
d) If a random person was selected, what would be the probability
that the person was a Broncos fan?
e) If a random person was selected, what would be the probability
that the person is not a Broncos fan and has 3-5 siblings?
f) If a random person was selected, what would be the probability
that the person is not a Broncos fan or has 0-2 siblings?
g)If a random a person was selected, what would be the probability
that the person was a Broncos fan and has 3-5 siblings?
In: Statistics and Probability
Q68 A branch of BNP-Paribas has an attractive credit programme. Customers meeting certain requirements can obtain a credit card called “BNP Wunder”. Local merchants in surrounding communities accept this card. The advantage is that with this card, goods can be purchased at a 2% discount and further, there is no annual cost for the card. Past data indicates that 35% of all card applicants are rejected because of unsatisfactory credit. Assuming that credit acceptance, or rejection, is a Bernoulli process, and samples of 15 applicants are made. [8 Marks]
(a) Develop a probability histogram for this situation.
(b) What is the probability that exactly three applicants will be rejected?
(c) What is the probability that at least three applicants will be rejected?
(d) What is the probability that more than three applicants will be rejected?
(e) What is the probability that exactly seven applicants will be rejected?
(f) What is the probability that at least seven applicants will be rejected?
(g) What is the probability that more than seven applicants will be rejected?
DO NOT WRITE THE ANSWERS - USE WORD FORMAT.
In: Statistics and Probability
In 2008, the per capita consumption of soft drinks in Country A was reported to be 19.35 gallons. Assume that the per capita consumption of soft drinks in Country A is approximately normally distributed, with a mean of 19.35 gallons and a standard deviation of 4 gallons. Complete parts (a) through (d) below.
a. What is the probability that someone in Country A consumed more than 14 gallons of soft drinks in 2008? The probability is nothing. (Round to four decimal places as needed.)
b. What is the probability that someone in Country A consumed between 9 and 10 gallons of soft drinks in 2008? The probability is nothing. (Round to four decimal places as needed.)
c. What is the probability that someone in Country A consumed less than 10 gallons of soft drinks in 2008? The probability is nothing. (Round to four decimal places as needed.)
d. 97% of the people in Country A consumed less than how many gallons of soft drinks? The probability is 97% that someone in Country A consumed less than nothing gallons of soft drinks. (Round to two decimal places as needed.)
In: Math
Use this table to answer the following questions.
| # of siblings | 0-2 | 3-5 | 6 or more | Total |
| Broncos Fan | 9 | 10 | 17 | 36 |
| Not a Broncos Fan | 2 | 6 | 3 | 11 |
| Total | 11 | 16 | 20 | 47 |
a) If a random a person was selected, what would be the
probability that the person was not a Broncos fan ?
b) Given that a person is a Broncos fan, what is the probability
that they have 6 or more siblings?
c) Given that a person has 3-5 siblings, what is the probability
that the person is not a Broncos fan?
d) If a random person was selected, what would be the probability
that the person was a Broncos fan?
e) If a random person was selected, what would be the probability
that the person is not a Broncos fan and has 3-5 siblings?
f) If a random person was selected, what would be the probability
that the person is not a Broncos fan or has 0-2 siblings?
g)If a random a person was selected, what would be the probability
that the person was a Broncos fan and has 3-5 siblings?
In: Math