Practice Quiz 8

Time:  20 minutes.  This quiz is open book, open notes.

1.    Identify the statements that must be false and state why.  Explain why the remaining statements can be true.

1. A random variable X has a mean of 3, a standard deviation of 2, and the probability that X is 9 or greater is 10%.
2. A random variable X is lognormally distributed with a mean of 20 and a standard deviation of 20.  The probability that X is less than zero is 1%.
3. Summary statistics for a batch of 30 data include a mean of 101.4, a standard deviation of 23.3, a fifth percentile of 13.0, and a 95th percentile of 179.9.
4. Every distribution has a median.
5. Every distribution has a mean.
6. The formula, "if today is a Tuesday, Thursday, or Saturday, then compute ; otherwise compute " is an estimator of the standard deviation of a statistical sample X₁, ..., X_n, provided n > 1.

2.    A statistical sample of 10 values is obtained from a lognormal distribution with mean 30 and standard deviation 50.  Does the skewness of the sample have to be positive?  Why or why not?

Scoring: The passing score is 95.

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