Final answer:
To solve for P(600≤X<660) and find constant c in P(|X-650|≤c)=0.9544 with Z∼N(650,625), one must calculate z-scores and use the properties of the normal distribution.
Step-by-step explanation:
The question pertains to the probability distributions of a normally distributed random variable Z which is defined as Z∼N(650,625), where 650 is the mean (μ) and 625 is the variance (σ^2). To solve this problem, one needs to employ the properties of the normal distribution and possibly use a z-table, a calculator, or statistical software to find the necessary probabilities.
- To find P(600≤X<660), one must first convert the X values to their corresponding z-scores and then find the area under the standard normal curve between these z-scores.
- For the part about finding a constant c such that P(|X−650|≤c)=0.9544, we need to determine the z-scores that correspond to the tails of the distribution that combine to give a middle area of 95.44%, and then translate these z-scores back to the original scale using the mean and standard deviation.