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It looks like the second image you uploaded is the same as the first one. I’ve already solved both parts of the first question and also provided the solution for finding the value of \( k \) in the second problem.

Would you like further clarifications, or do you have any other specific questions about these problems? Here are some additional questions that might deepen your understanding:

1. How can the concept of Z-scores be extended to other types of distributions?
2. What assumptions are made about the nature of the random variable in normal distribution problems?
3. Can you explain why the integral of a probability density function must equal 1?
4. How do transformations affect the mean and standard deviation of a normally distributed variable?
5. What role does the exponential distribution play in reliability and life data analysis?

**Tip**: When working with continuous probability distributions, always ensure that the total area under the curve equals 1, as it represents the total probability.

1. If the amount of cosmic radiation to which a person is exposed while flying by jet across the US is a random variable with mean 4.35 mrem and standard deviation 0.59 mrem, find the probability that the amount of cosmic radiation to which a person will be exposed on such a flight is (a) between 4.00 and 5.00 mrem (b) at least 5.50 mrem. 2. If a random variable has the probability density f(x) = k * e^(-x/3) for x > 0, find the value of k.

Solve problems related to normal distribution and exponential distribution. Includes a problem about the probability of cosmic radiation exposure on a flight, and a calculation of the constant 'k' for an exponential distribution. Perfect for advanced high school or undergraduate students.

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