Exam 2 Formula Sheet

Chapter 4

If A and B are disjoint (mutually exclusive), .

If a random phenomenon has k possible outcomes, all equally likely, then each individual outcome has probability .

The probability of any even A is .

If A and B are independent, .

In the language of random variables, if X has the distribution, then the standardized variable is a standard normal random variable having the distribution .

Suppose that X is a discrete random variable whose distribution is

Value of X /
Probability /

The mean of X is:

The variance of X is:

If events A, B, and C are disjoint (mutually exclusive), then .

For any two events A and B, .

The probability that both of two events A and B happen together can be found by . Here is the conditional probability that B occurs given the information in A occurs.

When , the conditional probability of B given A is .

Two events A and B that both have positive probability are independent if .

Chapter 5

If a count X has the binomial distribution , then .

The number of ways of arranging k successes among n observations is given by the binomial coefficient for k = 0, 1, 2, …, n.

If X has the binomial distribution with n observations and probability p of success on each observation, the possible values of X are 0, 1, 2,… , n. If k is any one of these values, the binomial probability is .

Let be the mean of an SRS of size n from a population having mean and standard deviation . The mean and standard deviation of are .

If a population has the distribution, then the sample mean of n impendent observations has the distribution.

Chapter 6

The confidence interval for a population mean will have a specified margin of error m when the sample size is .

Chapter 7

When the standard deviation of a statistic is estimated from the data, the result is called the standard error of the statistic. The standard error of the sample mean is .

Suppose that an SRS of size n is drawn from a population. Then the one-sample t statistic has the t distribution with n – 1 degrees of freedom.

Suppose that an SRS of size n is drawn from a population having unknown mean . A level C confidence interval for is .

  • is the point estimate
  • is the margin of error