Random Variables
A random variable that takes only whole number values.
What is a discrete random variable?
This shows the possible values of a random variable and their probabilities.
What is a probability distribution?
This type of distribution is shaped like a bell curve.
What is the normal distribution?
This sampling method gives each individual in the population an equal chance of being chosen, usually using a random number generator or lottery.
What is simple random sampling?
A single value used to estimate an unknown population parameter.
What is a point estimate?
This function describes the probability of a random variable taking on specific values.
What is a probability mass function (PMF)?
The square root of the variance is called this.
What is the standard deviation?
In a standard normal distribution, this value represents the mean.
What is 0?
A researcher selects every fifth person from a list of 1,000 people. This method is called what?
What is systematic random sampling?
The formula for estimating the population mean using a sample.
What is x̄ = ∑x/n?
Another name for the average of a random variable.
What is the expected value?
This measures how far values of a random variable are from the mean.
What is the variance?
The rule states that approximately 95% of the data in a normal distribution falls within how many standard deviations of the mean?
What is two (2) standard deviations?
A population consists of 5,000 people. The researcher divides them into male and female groups before randomly selecting 200 from each group. What sampling method is this?
What is stratified sampling?
The formula for estimating the standard deviation of a population using a sample is this.
What is s=sqrt(∑(x - x̄)2/n-1)
The sum of all probabilities in a discrete probability distribution must always equal this value.
What is 1?
The formula is Σ[(x - μ)²P(x)].
What is the variance formula?
The formula for converting a normal variable X to the standard normal variable Z is this (population).
Answer: What is Z = (X - μ) / σ?
A national study randomly selects 5 states and surveys every household in those states. What sampling method is this?
What is cluster sampling?
A sample of 10 students' test scores are: 75, 80, 85, 90, 95, 100, 85, 80, 90, 95. (point estimate)
What is x̄ = 87.5?
This type of random variable can take on any value within an interval and is described by a probability density function (PDF).
What is a continuous random variable?
If a discrete random variable has values 𝑥 with probabilities 𝑃(𝑥), this formula gives the expected value (mean).
What is E(X) = Σ[xP(x)]?
If a normal distribution has μ = 50 and σ = 10, what is the probability of randomly selecting a value greater than 70? (Use the standard normal table.)
What is 0.0228 (or about 2.28%)?
A formula used to determine the minimum sample size required for a given population size N and margin of error e in random sampling.
What is n=N/(1+Ne2)
A factory wants to estimate the average weight of products produced. A random sample of 50 items has an average weight of 2.8 kg with a sample standard deviation of 0.5 kg. What is the point estimate of the population mean?
What is μ=2.8 kg?