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True or False. Justify for full credit. (a) If A and B are any two events, then P(A AND B) = P(A) + P(B). (b) If the variance of a data set is 0, then all the observations in this data set must be identical. (c) A normal distribution curve is always symmetric to its mean. (d) When plotted on the same graph, a distribution with a mean of 60 and a standard deviation of 5 will look more spread out than a distribution with a mean of 40 and standard deviation of 8. (e) In a left—tailed test, the value of the test statistic is —2. The test statistic follows a distribution with the distribution curve shown below. If we know the shaded area is 0.03, then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.
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