1. The daily sale of chocolate in Othammarket is given below:

| Day | Sale (kg) |
|-----------|-----------|
| Monday | 140 kg |
| Tuesday | 50 kg |
| Wednesday | 60 kg |
| Thursday | 70 kg |
| Friday | 80 kg |
| Saturday | 90 kg |
| Sunday | 100 kg |

The average daily sale is 75 kg. Calculate the variance and the standard deviation of the above data.

2. What is the probability of getting a total of 7 or 11 when a pair of fair dice are tossed?

3. It is believed that 89% of the population is right-handed. In a random survey of 150 people, 135 claim to be right-handed. Calculate the z-test statistic.

4. Let \( X \) be a continuous random variable with the probability density function (PDF) given by:

\[
f(x) = \begin{cases}
\frac{k}{4 + x^2}, & \text{if } x \geq 0 \\
0, & \text{if } x < 0
\end{cases}
\]

(i) Find the value of \( k \).
(ii) Graph the PDF.
(iii) Calculate the probability \( P(0 < X < 1) \).
(iv) Determine the mean value of \( X \).

5. Let \( X \) be a normal random variable with a mean \( \mu = 20 \) and variance \( \sigma^2 = 25 \). Find the probability that the random variable \( X \) falls in the range [15, 30].