I just need to know if my thinking is correct aka I'm doing it correctly: sometimes the wording trips me up and I second guess myself. The following is the question/summary of it:
It's about the length of State of the Union Addresses, etc. They say the mean length for these addresses is 51.75 minutes and the standard deviation is 14.37 minutes. Assume the length of a State of the Union Address is normally distributed.
Now does normally distributed mean anything? Or can I just standardize whatever they ask about? For example:
What is the probability that the next State of the Union Address will be between 45 and 55 minutes long? What I did for this was standardized this then use the standard normal distribution cumulative probabilities table (which this question comes from the section in my book: full title of my section - Continuous Probability Distributions: The Normal Distribution).
Or do I do something else?
Thank you in advance.
Yes, you are told that the length of the address is normally distributed, that $X \sim Normal(\mu = 51.75, \sigma = 14.37)$. From this you can conclude that if the next address is randomly selected, the probability will follow $X$ and since $X$ is some normally distributed random variable, you can standardize this to $Z \sim Normal(\mu = 0, \sigma^2 = 1)$ and calculate the probability.