(i) To find μ, we use the standard normal distribution. Given P(X < 6.8) = 0.75, we find the corresponding z-value from the standard normal distribution table, which is approximately z = 0.674.

Using the standardization formula:

\(z = \frac{6.8 - μ}{0.25μ}\)

\(Substitute z = 0.674:\)

\(0.674 = \frac{6.8 - μ}{0.25μ}\)

Solving for μ:

\(0.674 imes 0.25μ = 6.8 - μ\)

\(0.1685μ = 6.8 - μ\)

\(1.1685μ = 6.8\)

\(μ = \frac{6.8}{1.1685} \approx 5.82\)

(ii) To find P(X < 4.7), we standardize using the mean and standard deviation:

\(P(X < 4.7) = P\left( z < \frac{4.7 - 5.82}{1.4548} \right)\)

\(= P(z < -0.769)\)

Using the standard normal distribution table, \(P(z < -0.769) = 1 - 0.7791 = 0.221\)