The Pew Internet and American Life Project reported in 2004 that “17% of current music down loaders say they are using paid services”. Consider a random sample of 400 music down loaders. Compute the probability that X equals the mean of X where X is the number of current music down loaders (You can use appropriate program). Find the mean of X. Find the probability?
In: Statistics and Probability
The probability is 0.4 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. In nine traffic fatalities, find the probability that the number, Y, which involve an intoxicated or alcohol-impaired driver or nonoccupant is
a. exactly three; at least three; at most three.
b. between two and four, inclusive.
c. Find and interpret the mean of the random variable Y.
d. Obtain the standard deviation of Y.
In: Statistics and Probability
The following is the transition probability matrix of a Markov chain with states
1,2,3,4
⎛⎞
.4 .3 .2 .1 P=⎜.2 .2 .2 .4⎟ ⎝ .25 .25 .5 0 ⎠
.2 .1 .4 .3
(a) find the probability that state 3 is entered before state
4;
If X0 = 1
(b) find the mean number of transitions until either state 3 or
state 4 is entered.
In: Statistics and Probability
Problem 7-28 A student selects his answers on a true/false examination by tossing a coin (so that any particular answer has a .50 probability of being correct). He must answer at least 70% correctly in order to pass. Find his probability of passing when the number of questions is
(a) 10 Pr=
(b) 20 Pr=
(c) 50 Pr=
(d) 100 Pr=
In: Statistics and Probability
a) What is the probability of rolling a 5 with a balanced die?
b) Find the number of ways in which a person can select 3 stocks from a list of 5 stocks?
c) What is probability of drawing a 5 from a well shuffled deck of 52 playing cards?
d) In how many ways can a principal choose 3 of 45 members to review a student grade appeal?
In: Statistics and Probability
In a waiting line situation, arrivals occur at a rate of 3 per minute, and the service times average 12 seconds. Assume the Poisson and exponential distributions.
|
a. |
What is λ? What is μ? |
|
b. |
Find average number of units in the system. |
|
c. |
Find average time in the waiting line. |
|
d. |
Find probability that there is one person waiting. |
|
e. |
Find probability an arrival will have to wait. |
In: Statistics and Probability
A box in a certain supply room contains four 30W lightbulbs, five 60W lightbulbs, and six 70W lightbulbs. Suppose that four lightbulbs are randomly selected. 1) What is the probability that at least one lightbulb of each type is selected? 2)Find the expected number of lightbulbs (incorrect ones) that need to be selected before a 60W or 70W lightbulb is selected. Show this by building a probability table.
In: Statistics and Probability
Let the number of aberrations in the production of a large scale
lens have a Poisson distribution. We want the probability that a
given lens contains at most one aberration to be greater than
0.99.
a) Find the largest value of the mean that this distribution can
take.
b) Assume the mean is µ = 0.11. Determine the probability that a
batch of 5 lens will have at least two lenses with at least one
defect each.
In: Statistics and Probability
The probability is 0.3 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. In eight traffic fatalities, find the probability that the number, Y, which involve an intoxicated or alcohol-impaired driver or nonoccupant is a. exactly three; at least three; at most three. b. between two and four, inclusive. c. Find and interpret the mean of the random variable Y. d. Obtain the standard deviation of Y.
In: Math
The probability is0.45 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. In
seven traffic fatalities, find the probability that the number, Y, which involve an intoxicated or alcohol-impaired driver or nonoccupant is
a. exactly three; at least three; at most three.
b. between two and four, inclusive.
c. Find and interpret the mean of the random variable Y.
d. Obtain the standard deviation of Y.
In: Math