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Apply distributions across unfamiliar problems: original cases with explanations after your first response.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
Read the probability weights and distinguish a single outcome from a long-run average. Use only the distributional assumptions that the question supplies.
A discrete random variable takes values 0,2,5 with probabilities .2,.5,.3. What is its expected value?
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A probability distribution assigns probabilities .15,.25,p,.2 to its four outcomes. What is p?
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A normal distribution has mean 50 and SD 8. What value is two standard deviations below the mean?
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A distribution is normal with mean 100. What percent of its values lie below 100?
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For a normal distribution, approximately 68 percent lies within one SD of the mean. Approximately what percent lies above one SD above the mean?
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Assume approximately 95 percent of a normal population lies within two SDs of its mean. Out of 800 observations, approximately how many lie outside this interval?
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A population has SD 6. Y is obtained by multiplying each value by 4 and subtracting 8. What is the SD of Y?
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For a continuous uniform distribution on [2,10], what is the probability of a value between 5 and 7?
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A fair die is rolled twice independently. Let X count the number of sixes. What is P(X=2)? Enter a fraction.
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The mean of a normal distribution is 30 and its SD is 5. A value of 42.5 is how many SDs above the mean?
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A distribution gives P(X<=3)=.65 and P(X=3)=.15. What is P(X<3)?
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X takes values 0 and 4 with probabilities .75 and .25. Using variance E(X squared)-(E(X)) squared, what is its variance?
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Confirm that weights total one and translate standard-deviation units back to the original scale; symmetry alone does not determine every interval probability.