Thank you I have three errands to take care of in the Administration Building. L

Question

Thank you

I have three errands to take care of in the Administration Building. Let X_i = the time that it takes for the ith errand (i = 1, 2, 3), and let X_4 = the total time in minutes that I spend walking to and from the building and between each errand. Suppose the X_i' s are independent, and normally distributed, with the following means and standard deviations: mu_1 = 15, sigma, = 4, mu_2 = 5, sigma_2 = 1, mu_3 = 8, sigma_3 = 2, mu_4 = 12, sigma_4 = 3. I plan to leave my office at precisely 10:00 a.m. and wish to post a note on my door that reads, "I will return by t a.m." What time t should I write down if I want the probability of my arriving after t to be .01?

Explanation / Answer

here mean time of activities =(15+5+8+12) =40

and std deviaiton =(42+12+22+32)1/2=(30)1/2 =5.477

also from normal distribution for 0.01 probabilty after time t, he should have 99% confidence that he be back in office before that

for 99% , z =2.3263

hence total time =mean+Z*std deviation =40+2.3263*5.477 =52.74 minutes =53 minutes approx

hence time he should be back =10:53 AM

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