(a) For normal distribution curve mean, median and mode coincide. Also every distribution is divided into two equal parts by its median, i.e. symmetric about median. Since for a normal distribution curve mean is same as median, the distribution is symmetric about its mean.

(b) If all the observations in a data set are identical, then its arithmetic mean is also has the same value of the observations. Therefore, it can be observed that all the mean deviations from the observations in the data set are zero, so as its variance is also zero.

(c) Since A and AC are disjoint, the probability of their intersection must be equal to zero, not equal to 1.

(d) If p-value is less than the level of significance α, it indicates that the test statistic fall in the rejection region, so we have sufficient evidence to reject the null hypothesis.

(e) The volume of a milk jug represents a continuous data, since it can take any of the values between the given limits.

2. The shaded cells in the following table indicate the calculated values.

Checkout Time (in minutes)
Frequency, f
Relative Frequency
1.0 - 1.9
2
0.08
2.0 - 2.9
8
0.32
3.0 - 3.9
10
0.40
4.0 - 5.9
5
0.20
Total
25
1.00