Question

A shipping company handles containers in three different sizes. 1. 27 43 (3 x 3 x 3) 2. 125 ft 3 3. 512 ft 3 Let X; (i = 1, 2, 3) denote the number of type i containers shipped during a given week. With u; = E(X;) and 0,2 = V(X;), suppose that the mean values and standard deviations are as follows. 41 = 450 42 = 400 43 = 50 91 = 12 02 = 8 03 = 10 Suppose that the X;'s are independent with each one having a normal distribution. What is the probability that the total volume shipped is at most 100,000 ft? (Round your answer to four decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

Nar (Y) 도 MV XIN NC 450,122), X, NC 400,8?), solution or *3 ^ NC 50,102) Total notume Let Yt be the random variable that denotes the total volume. Y= 24 %, + 12542 +512 X3 ELY) = 27 ECXI) + 125 E(X) +512 EcX3) 87450 242 Varcxu + 1252 Vari (42) + 512² vare X3) 27319346 & AKN yo NC 87450, 243193462 PCYB 5 100,000) EPL145075 = P(Z5100000-84450 ZE Y-ECU) ✓27319376 Svarto ; Z~Neo, 1) = P(Z L 12250 24319376 PCZ12.34369288) = 009904531 0.9904 tot ovat