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1 . 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 .
2 . Choose the best answer . Justify for full credit .
( a ) A study was conducted at a local college to analyze the average GPA of students graduated from UMUC in 2016 . 100 students graduated from UMUC in 2016 were randomly selected , and the average GPA for the group is 3.5 . The value 3.5 is a