Question4. A study of the weights of the brains of Swedish men varies according to a distribution that is approximately Normal with mean 1400 grams and standard deviation 20 grams.
If two Swedish men named Nordal and Hector are selected, what is the probability that Nordal's brain weighs at least 15 grams more than Hector's? (For full credit, show ALL work, including making a picture).

Studdy Solution
Calculate the probability: - Standardize the variable: $P(Z \geq 15)$. - Convert to standard normal: $P\left(\frac{Z - 0}{\sqrt{800}} \geq \frac{15}{\sqrt{800}}\right)$. - Calculate the z-score: $z = \frac{15}{\sqrt{800}} \approx 0.5303$. - Use the standard normal distribution table to find $P(Z \geq 0.5303)$. - This is equivalent to $1 - P(Z \leq 0.5303)$. - From the standard normal table, $P(Z \leq 0.5303) \approx 0.7023$. - Therefore, $P(Z \geq 0.5303) = 1 - 0.7023 = 0.2977$.
The probability that Nordal's brain weighs at least 15 grams more than Hector's is approximately:
$$\boxed{0.2977}$$