As the owner of a sailboat, you conduct sailing trips for couples (one husband a

Question

As the owner of a sailboat, you conduct sailing trips for couples (one husband and one wife). Unfortunately, the Texas Parks and Wildlife has a 620 pound limit on the total weight of all your passengers (not counting yourself). The weight of husbands is known to have a mean of 160 Jfcs. and standard deviation of 15 JbSc whereas wives have a mean weight of 130 lbs and standard deviation of 10 lbs. If you sign up 2 couples (2 husbands and 2 wives), answer the following questions. You may assume that the weights of husbands and wives are independent and normally distributed. what is the average total weight of the 2 couples on the sailboat? What is the variance of the total weight of the 2 couples? c. |What is the standard deviation of the total weight of the 2 couples? d. If the game warden showed up (with scales to weigh your passengers) right when you were getting ready to go sailing with your 2 couples, what is the probability that your 2 couples EXCEED the maximum weight limit of 620 lbs? Draw a picture of the total weight of the 2 couples to help you calculate this probability.

Explanation / Answer

answer of part (a)

average weight of 2 couples =2(160+130)=580

answer of part (b)

variance of husband=15*15=225

variance of wife=10*10=100

so variance of a couple=225+100=325

therefore variance of two couple=2*325=650

answer of part (c)

standard deviation of 2 couple= sqrt(variance of two couple)=sqrt(650)=25.49

answer of part(d)

the mean of two couple is 580 and standard deviaion=25.49

we calculate z

here z=(620-580)/25.49=1.5689

p(z>1.5689)=1-0.9417=0.0583

requied probability=0.0583

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