04:54
Probability with Applications in Engineering, Science, and Technology
A professor has three errands to take care of in the Administration Building. Let $X_{i}=$ the time
that it takes for the $i$ th errand $(i=1,2,3),$ and let $X_{4}=$ the in minutes that spends walking to and from the building and between each errand. Suppose the $X_{i}$ s are independent, normally distributed, with the following means and standard deviations: $\mu_{1}=15, \sigma_{1}=4$ $\mu_{2}=5, \sigma_{2}=1, \mu_{3}=8, \sigma_{3}=2, \mu_{4}=12, \sigma_{4}=3 .$ She plans to leave her office at precisely $10 : 00$ a.m. and wishes to post a note on her door that reads, "I will return by $t$ a.m." What time $t$ should she write down if she wants the probability of her arriving after $t$ to be .01$?$