Which is more likely to occur that a randomly selected adult will complete the test in less than 43 minutes or that when 50 randomly selected adults take the test, the mean time used to complete the test will be less than 43 minutes?

Let $X$ be the time it takes for a single randomly selected adult to complete the test. $X$ follows a normal distribution with $\mu = 46.2$ and $\sigma = 8$. We want to find $P(X < 43)$.

The formula for a Z-score is $Z = \frac{X - \mu}{\sigma}$.

From the Z-table, $P(Z < -0.4) \approx 0.3446$.

Let $\bar{X}$ be the mean time for a sample of $n=50$ randomly selected adults. According to the Central Limit Theorem, $\bar{X}$ follows a normal distribution with:

• Mean of the sample means, $\mu_{\bar{X}} = \mu = 46.2$ minutes.
• Standard deviation of the sample means (standard error), $\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}$.

We want to find $P(\bar{X} < 43)$.

The formula for the Z-score of a sample mean is $Z = \frac{\bar{X} - \mu_{\bar{X}}}{\sigma_{\bar{X}}}$.

$P(\bar{X} < 43) = P(Z < -2.83)$ (rounding Z-score to two decimal places for table lookup) From the Z-table, $P(Z < -2.83) \approx 0.0023$.