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variable is a variable that has a single numerical? value, determined by? chance, for each outcome of a procedure.

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random variable

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random variable has infinitely many values associated with measurements.

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continuous random variable

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The .......
of a discrete random variable represents the mean value of the outcomes.

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expected value

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<0.05

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unlikely/ unusual

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Which of the following is not a requirement of the binomial probability? distribution?

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the trials must be dependent

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In the binomial probability? formula, the variable x represents the

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probability of getting X successes among n trials

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?If, under a given? assumption, the probability of a particular observed event is extremely? small, we conclude that the assumption is probably not correct.

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rare event rule

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The? _______ of a discrete random variable represents the mean value of the outcomes.

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expected value

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To determine the probability that among the 17 offspring peas ,at least 16 have green pods, use the fact that....

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P(at least 16)=p(16)+p(17)

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says that the range is about four times the standard deviation

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range rule of thumb

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4*standard deviation

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range rule of thumb

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Why must a continuity correction be used when using the normal approximation for the binomial? distribution?

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The normal distribution is a continuous probability distribution being used as an approximation to the binomial distribution which is a discrete probability distribution.

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Sample means, variances and proportions

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unbiased estimators

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Sample medians, ranges and standard deviations

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biased estimators

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a variable (typically represented by x) that has a single numerical value, determined by chance, for each outcome of a procedure

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random variable (X)

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a description that gives the probability for each value of the random variable, often expressed in the format of a graph, table, or formula

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probability distribution

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a EXACT number of values or countable number of values

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DISCRETE random variable

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infinitely many values, and those values can be associated with measurements

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continuous random variable

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mean formula

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mean=X*the probability of X

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standard deviation=

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square root of ......(x-mean)^2 * the probability of (x)

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x successes among n trials is an unusually high number of successes if

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p(X or more)<0.05

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x successes among n trials is an unusually low number of successes if

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p(x or fewer)<0.05

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-The procedure has a fixed number of trials.
-The trials must be independent. (The outcome of any individual trial doesn't affect the probabilities in the other trials.)
-Each trial must have all outcomes classified into two categories (commonly referred to as success and failure).
-The probability of a success remains the same in all trials.

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binomial distribution

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p(s)=p

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probability of success

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denotes a specific number of successes in n trials,

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X

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denotes the fixed number of trials.

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n

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denotes the probability of success in one of the n trials.

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p

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denotes the probability of getting exactly x successes among the n trials.

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p(x)

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When sampling without replacement, consider events to be independent if

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n<0.05n

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range rule of thumb:
maximum usual value
minimum usual value

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n+2(standard deviation)
n-2(standard deviation)

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bell shaped- empirical rule when

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np>5

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The Poisson distribution is sometimes used to approximate the binomial distribution when

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n=large
p=small

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Its graph is bell-shaped.
Its mean is equal to 0 (? = 0).
Its standard deviation is equal to 1 (? = 1).

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STANDARD NORMAL distribution

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1. The total area under the curve must equal 1.
2. Every point on the curve must have a vertical height that is 0 or greater. (That is, the curve cannot fall below the x-axis.)

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density curve

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use area to find....

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probability

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normal distribution: how to find areas on calc

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normal CDF

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z=

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x-mean/s

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The points do not lie reasonably close to a straight line.
The points show some systematic pattern that is not a straight-line pattern.

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NOT a normal distribution

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Step 1. First sort the data by arranging the values in order from lowest to highest.
Step 2. With a sample of size n, each value represents a proportion of 1/n of the sample. Using the known sample size n, identify the areas of 1/2n, 3/2n, and so on. These are the cumulative areas to the left of the corresponding sample values.
Step 3. Use the standard normal distribution (Table A-2 or software or a calculator) to find the z scores corresponding to the cumulative left areas found in Step 2. (These are the z scores that are expected from a normally distributed sample.)
Step 4. Match the original sorted data values with their corresponding z scores found in Step 3, then plot the points (x, y), where each x is an original sample value and y is the corresponding z score.
Step 5. Examine the normal quantile plot and determine whether or not the distribution is normal.

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Manual Construction of a Normal Quantile Plot

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is the distribution of all values of the statistic when all possible samples of the SAME SIZE N are taken from the SAME POPULATION

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the sampling distribution of a statistic

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THE sampling distribution of the sample? mean

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normal distribution NOT SKEWED TO LEFT OR RIGHT

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the distribution of sampling variance

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SKEWED NOT NORMAL

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MEADIAN

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BIASED ESTIMATOR

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says that the computed values of the average will be distributed according to the normal distribution (commonly known as a "bell curve").

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CENTRAL limit theorem