Category A
This type of random variable takes a fixed set of possible numerical values that describe the outcomes of some chance process.
Discrete Random Variable
This table gives possible values and their probabilities for a random variable
probability distribution
This is also know as an expected value of a discrete random variable and is found by multiplying each possible value by it's probability and then adding up all the products.
Mean of a discrete random variable
this type of random variable takes all values in an internal of numbers
This takes all values in an interval of numbers of that describe the outcomes of some chance process.
continuous random variable
20% of viewers watch 60 Minutes. Estimate the probability that 35 or fewer in a random sample of 200 households are watching 60 minutes.
0.1660
What is the name of Ms Martinez's dog?
Moon :)
T or F:
If there is a correlation, that proves causation.
FALSE
What does it mean for events to be independent?
One probability does not affect the other
These conditions must be met to confirm a binomial setting exists.
Binary
Independent
Numbers
Success
In a large university, 30% of the incoming freshmen elect to enroll in a Personal Finance course offered by the university. Find the probability that of 800 randomly selected incoming freshmen, at least 260 have elected to enroll in the course.
0.0662
What does n stand for in the binomial formula?
The total number of trials
This is how the standard deviation of a binomail random variable is caclculated.
sigma_{x}=sqrt(np(1-p)
When this condition is met, you can approximate the binomial distribution with a normal distribution.
Write the name and the formulas
Large Counts Condition
np ≥ 10
n(1-p)≥ 10
If you're using a normal distribution, how do you find the area between two values?
Subtract them
How can you tell if a probability distribution is valid?
1. The probabilities add up to 1
2. Each probability is between 0 and 1
This is how the mean of a binomial random variable is calculated.
mu_{x}=np
A marketing survey compiled data on the number of cars in households. If X=the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, then X has the following probability distribution:
x 0 1 2 3 4 5
P(x) 0.24 0.37 0.20 0.11 0.05 0.03
The probability that a radomly chosen household has at least two cars.
Add all probabilities for each value of x that considered a "success"
0.20+0.11+0.05+0.03 = 0.39
A marketing survey compiled data on the number of cars in households. If X=the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, then X has the following probability distribution:
x 0 1 2 3 4 5
P(x) 0.24 0.37 0.20 0.11 0.05 0.03
The expected value of the number of cars in a randomly selected household is:
Find the weighted average. Take the value times the probability that value will occur and add up all of the products.
0(0.24)+1(0.37)+2(0.20)+3(0.11)+4(0.05)+5(0.03)=1.45
Ms Martinez has a life-sized cut out of this celebrity.
Danny DeVito
In the town of lakevill, the nuber of cell phones in a household is a random variable W with the following probability distribution.
Value (W) 0 1 2 3 4 5
Probability (P) 0.1 0.1 0.25 0.3 0.2 0.05
The mean of the number of cell phones in a randomly selected house:
Mean:
0(0.1) +1(0.1) +2(0.25) +3(0.3)+4(0.2)+5(0.05) = 2.55
It is known that about 90% of the widgets made by Buckley Industries meet specifications. Every hour a sample of 18 widgets is selected at random for testing and the number of widgets that meet specifications is recorded. What is the approximate mean and standard deviation of the number of widgets meeting specifications.
Mean:
μ x = (18)(.9)=16.2
Standard Deviation:
sqrt(18(.9)(1-.9))=1.273
What is standard deviation?
The typical distance from the mean
A raffle sells tickets for $10 and offers a prize of $500, $1000, or $2000. Let C be a random variable that represents the prize in the raffle drawing. The probability distribution of C is given below:
C $0 $500 $1000 $2000
P(C) 0.60 0.05 0.13 0.11
The expected profit when playing the raffle is:
Expected value is the same thing as the mean, so you calculate the expected profit by multiplying the value of C times the probability of C, and summing up the products.
(0)(.6)+(500)(.05)+(1000)(.13)+(2000)(.11)=375
Let the random variable X represent the amount of money Carl makes tutoring statistics students in the sumer. Assume that X is Normal with mean $240 and standard deviation $60. The probability is approximately 0.6 that, in a randomly selected summer, Carl will make less than about:
255.20