SOLUTION: In this problem , it is recommended that you use a tree diagram . The national sleep foundation found that 30% of people surveyed prefer a firm mattress while 70% prefer a soft one

Question 1085180: In this problem , it is recommended that you use a tree diagram . The national sleep foundation found that 30% of people surveyed prefer a firm mattress while 70% prefer a soft one. Of the 30% who prefer firm mattress , 20% prefer serta, 30% prefer Klein and 50% prefer sleep number . Of the 70% who prefer soft , 25% prefer serta , 35% prefer Klein and 40% prefer sleep number . If a random mattress(soft or firm) is selected , calculate the percentage of people who select a Klein mattress.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
here's my worksheet.

$$$

top of the tree is mattress.

this gets split into 30% firm and 70% soft

firm gets split into 20% serta 30 klein 50% sleep number

soft gets split into 25% serta 35% klein 40% sleep number.

the ratio, or proportion in each branch is the ratio in each step of the branch multiplied by each other.

for example, ratio of serta in the firm branch is .3 * .2 = .06 and ratio of serta in the soft branch is .7 * .25= .175

the total ratio, or proportion, of serta is .06 + .175 = .235

likewise, the ratio, or proportion, of klein is .09 + .245 = .335

this means that 33.5% of the people selected a klein.

percent = (ratio or proportion) * 100

(ratio or proportion) = percent / 100

.335 ratio = 33.5%

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