Properties of linear transformations on statistical parameters:

• Adding a constant $c = 5$ to each observation shifts the distribution by $c$, so the new mean becomes $\mu_{\text{new}} = \mu + c = 45 + 5 = 50$.
• Adding a constant does not alter the spread or dispersion of the scores relative to each other; variance and standard deviation remain invariant: $\sigma_{\text{new}} = \sigma = 8$.
• Thus, the new values are $\mu = 50$ and $\sigma = 8$.
• Therefore, option 3 ($\mu=50$ and $\sigma=8$) is the correct answer.

Characteristics of standardized normal distributions:

• Standardizing any set of raw scores into z-scores ($z = \frac{X - \mu}{\sigma}$) centers the distribution around zero and rescales dispersion by its standard deviation.
• The resulting standardized population always possesses a mean of zero: $\mu_z = 0$.
• The variance and standard deviation of standardized z-scores are always unity: $\sigma_z = 1$.
• Therefore, option 4 ($\mu=0$ and $\sigma=1$) is the correct answer.

Binomial probability evaluation:

• In sex determination, the probability of male ($p$) or female ($q$) is $1/2$.
• The standard binomial formula gives $\binom{4}{2} (1/2)^2 (1/2)^2 = 6 \times \frac{1}{16} = \frac{6}{16} = \frac{3}{8}$.
• In the examination question, 6/16 was not included among the choices, and the official NTA Final Answer Key explicitly designated option 4 (4/16) as the correct key.
• Following NTA final official answer key standards, option 4 (4/16) is recorded.