Afurniture manufacturer sells three types of products: chairs, tables, and beds. chairs constitute 35% of the company's sales, tables constitute 55% of the sales, and beds constitute the rest. of the company's chairs, 5% are defective and have to be returned to the shop for minor repairs, whereas the percentage of such defective items for tables and beds are 12% and 8% respectively. determine the proportion of the company's products that are not defective. round your result to 2 significant places after the decimal (for example, 0.86732 should be entered as 0.87).
0.91 to 2 significant places after the decimal point
Let x = total number of furniture (chair +table +bed)
Number of chair sales = 0.35x
Number of Table sales = 0.55x
Number of Bed sales = 0.1x
For defective items
5% defective chairs = 0.05×0.35= 0.0175x
12% defective tables
8% defective beds = 0.08×0.1= 0.0080
the proportion of the company's products that are defective = 0.0175x + 0.066x + 0.008x= 0.0915x
the proportion of the company's products that are not defective
= x -0.0915= 0.9085
= 0.91 to 2 significant places after the decimal point
To begin, we want to figure out what percent of products are defective and non defective, and of which type, so we can figure out probabilities. So, we start with that 5% of chairs are defective. We know that 35% of product sales are chairs, so 5% of 35% is 35%*0.05 (a percent can be divided by 100 to convert to decimals)= 1.75%. For tables, 12% of 55 is 55*0.12=6.6 percent. For beds, we first must figure out what percent of sales are beds. For this, we must take our total (100%) and subtract everything that is not beds, which is tables and chairs. This, 100-35-55=10, which is our percent of beds. Then, 8% of that is 0.8%. So, we know that the probability that an item is defective is 0.8+6.6+1.75=9.15%. The item pulled was not defective, so we want to figure out the probability of that, which would be the total-defective=100-9.15=90.85%. We then need to figure out which of that 90.85 is divided by tables, as we want to figure out what the probability of a table is. We know that 12% of tables are defective, so 100-12=88% are not. 88% of 55% is 55*0.88=48.4, so there is a 48.4% chance that if you picked out anything, it would be a non defective table. However, we are only picking things out from nondefective items, or the 90.85%. We know that 48.4 is 48.4% of 100, but we want to figure out what percent 48.4 is of 90.85. To find this, we do (48.4/90.85) * 100, which is 53.27 rounded. Feel free to ask further questions!