(b) What is the probability the random variable will assume a value between 55 and 85 ? (Round your answer to three decimal places.) (c) What is the probability the random variable will assume a value between 65 and 75 ? (Round your answer to three decimal places.)

To find the probabilities, you typically would need the mean and standard deviation of the random variable, as well as the distribution it follows (e.g., normal distribution). Once you have those, you could use techniques like the z-score formula or a probability density function to calculate the probabilities for the given ranges. If you’re working with a normal distribution, first, calculate the z-scores for the given values. For 55 and 85, you would find the z-scores, look them up in the standard normal distribution table, and subtract to find the probability between those values. The same process applies for the interval from 65 to 75. Each step must be handled carefully to ensure accuracy in your final rounded probabilities.