I'm doing some math homework and I can't quite figure out how to solve this one.
The length of time to complete a door assembly on an automobile factory assembly is normally distributed with a mean of 6.7 and a standard deviation of 2.2 minutes. For a door selected at random, what is the probability the assembly time will be: a) 5 minutes or less? b) 10 minutes or more? c) between 5 and 10 minutes?
The Z score of 5 is -0.7727 (rounded to 4 sig figs), and the z-score of 10 is 1.5. How can I use this data to answer a and b? If I use my calculator it gives me
a: .7802; b: .2198; c: .7134;
Is this correct? It feels wrong to me since and b are just complete opposites. Thank you in advance!!
Why do you want to compute the Z-score? You have a random variable $X \sim N(6.7, 2.2)$ and you want to compute the probabilities $P(X \leq 5)$, $P(X \leq 10)$ and $P(5 \leq X \leq 10)$, which you can compute with the CDF.