True or False. Justify with explanation

(a) If A and B are any two events, then P(A AND B) ≤ P(A OR B).

(b) If the variance of a data set is 0, then all the observations in this data set must be zero.

(c) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set.

(d) When plotted on the same graph, a distribution with a mean of 60 and a standard deviation of 5 will look less 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 0.97, then we do not have sufficient evidence to reject the null hypothesis at 0.05 level of significance.