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Sampling Distribution Models Sampling distributions of Proportions and Means C.L.T

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The different models The Normal Model – a set of data with mean and STDDEV The Probability (random variable) Model – random variable, each out come has different p Bernoulli trials, success failure The Binomial Model –; approx w/ N( ) order doesnt matter constant p, two outcomes p and q, nCx The Geometric Model – order does matter constant p, two outcomes p and q;

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Imagine: What would happen if we drew many random samples of the same size from the same population and considered the values for our sample statistic? Click on wand for web page

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Assumptions & Conditions: Independence Assumption a- Randomization Condition and b- 10% condition Sample Size Assumption Sample Size Assumption – need large enough sample a- success/ failure condition np and nq both 10 Sample Distribution of a Proportion ( )

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Sample Distribution of a Proportion ( ): Normal Model a- mean = b- stddev = Sample Size Assumption Sample Size Assumption – need large enough sample a- success/ failure condition np and nq both 10

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15) Based on past experience, a bank believes that 7& of the people who receive loans will not make payments on time. The bank has recently approved 200 loans. a) What are the mean and stddev of the proportion of clients in this group who may not make timely payments?

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Based on past experience, a bank believes that 7& of the people who receive loans will not make payments on time. The bank has recently approved 200 loans. b) What assumptions underlie your model? Are the conditions met? Explain.

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Based on past experience, a bank believes that 7& of the people who receive loans will not make payments on time. The bank has recently approved 200 loans. c) Whats the probability that over 10% of these clients will not make timely payments?

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37) Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and stddev 16 days. a) What percentage of pregnancies should last between 270 and 280 days?

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Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and stddev 16 days. b) At least how many days should the longest 25% of all pregnancies last?

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Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and stddev 16 days. c) Suppose a certain obstetrician is currently providing prenatal care to 60 pregnant women. Let y-bar be the mean length of their pregnancies. According to the CLT, whats the distribution of the sample mean, y-bar? Specify the model, mean and stddev.

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Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and stddev 16 days. d) Whats the probability that the mean duration of these patients pregnancies will be less than 260 days?

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