Problem 1: Envelopes come manufactured with glue afixed at three separate locati
ID: 3314756 • Letter: P
Question
Problem 1: Envelopes come manufactured with glue afixed at three separate locations on the flap. After wetting the glue, all that is required to have the envelope seal is for two of the glue spots to stick to the envelope. The automatic envelope stuffing and sealing machine in the office will insert a letter into one of these envelopes and then wet the three glue spots. The amount of water applied to each glue spot follows a normal distribution with mean of 10 ml and standard deviation of 1.5 ml. If less than 8.5 ml of water is applied the glue will not activate (no adherence). If more than 13 ml of water is applied the glue will wash away (no adherence) Part 1a: Part 1b: What is the probability that an envelope will seal? On average, what percentage of envelopes fail to seal?Explanation / Answer
1a) probabilty that envelop will wash away =P(8.5<X<13)=P((8.5-10)/1.5<Z<(13-10)/1.5)=P(-1<Z<2) =0.9772-0.1587
=0.8186
1b)% of envelop fail to glue =(100-% of envelop that seal) =(100-81.86)% =18.14%