Final answer:
The problem involves finding the value of 'k' in a normal distribution where the probability of X being greater than 'k' is 0.9346. Given the high probability and understanding of normal distributions, 'k' must be below the mean, which is 300, making option b (k<350) correct. There's not enough information to determine the relationship between 'k' and 250.
Step-by-step explanation:
The student is working with a normal distribution problem where the random variable X follows a normal distribution denoted by X∼N(300,6400). Here, the mean (μ) is 300, and the variance (σ^2) is 6400, which means the standard deviation (σ) is the square root of 6400, which is 80. The question states that the probability that X is greater than some value k is 0.9346, meaning P(X>k)=0.9346. To find the value of k, we would use the normal distribution table or a calculator with the inverse normal function to find the z-score that corresponds to the cumulative probability of (1-0.9346) = 0.0654. We transform this z-score to the value k using the formula k = μ + z*σ.
Without the need to calculate k, we can determine the relationship between k and 350 by the nature of the normal distribution and the given probability. Because 0.9346 is a large probability, it means that k should be a value that is less than the mean; thus k must be less than 300, not 350. None of the reference information provided helps us calculate the exact value of k, so we rely on our understanding of normal distributions to answer the question. Since the probability is high (more than 0.5), and given that the normal distribution is symmetric, the value of k must be smaller than the mean (300), placing it somewhere below 300 and making option b (k<350) the correct one. We do not have enough information to comment on the relationship between k and 250, hence options a and c cannot be concluded, and d is not directly supported by the given information.