(a) To find the probability that a randomly chosen cyclist has a time less than 74 minutes, we use the standard normal distribution. The standardization formula is:

\(Z = \frac{X - \mu}{\sigma}\)

where \(X = 74\), \(\mu = 62.3\), and \(\sigma = 8.4\). Substituting these values, we get:

\(Z = \frac{74 - 62.3}{8.4} = 1.393\)

We find \(P(Z < 1.393)\) using the standard normal distribution table, which gives us:

\(P(X < 74) = 0.918\)

(b) To find the probability that 4 randomly chosen cyclists all have times between 50 and 74 minutes, we first find the probability for one cyclist:

\(P(50 < X < 74) = P\left(\frac{50 - 62.3}{8.4} < Z < \frac{74 - 62.3}{8.4}\right)\)

\(P(-1.464 < Z < 1.393)\)

Using the standard normal distribution table, we find:

\(\Phi(1.393) = 0.9182\)

\(\Phi(-1.464) = 0.0718\)

\(P(-1.464 < Z < 1.393) = 0.9182 - 0.0718 = 0.8464\)

The probability that all 4 cyclists have times between 50 and 74 minutes is:

\((0.8464)^4 = 0.514\)