Explanation: This is an application of conditional probability; P(E1,E2)=P(E1|E2)P(E2), so P(E1|E2) = P(E1,E2) / P(E2) P(E1,E2,E3) / P(E2,E3) If the events are A and B respectively, this is said to be "the probability of A given B". It is commonly denoted by P(A|B), or sometimes PB(A). In case that both "A" and "B" are categorical variables, conditional probability table is typically used to represent the conditional probability.
Question : Which of the following is an example of Gaussian distribution application? 1. If the average man is 175 cm tall with a variance of 6 cm, what is the probability that a man found at random will be 183 cm tall? 2. If the average man is 175 cm tall with a variance of 6 cm and the average woman is 168 cm tall with a variance of 3cm, what is the probability that the average man will be shorter than the average woman? 3. Access Mostly Uused Products by 50000+ Subscribers order to ensure that the 99% of all cans have a weight of at least 250 grams? 4. 1 and 2 only 5. Both 1 and 2
Explanation: Normal distribution is without exception the most widely used distribution. It also goes under the name Gaussian distribution. It assumes that the observations are closely clustered around the mean, ?, and this amount is decaying quickly as we go farther away from the mean.
Question : It was found that the mean length of parts produced by a lathe was . mm with a standard deviation of . mm. Find the probability that a part selected at random would have a length between 20.03 mm and 20.08 mm
X = length of part (a) 20.03 is 1 standard deviation below the mean; 20.08 is 20.08?20.050.02=1.5 standard deviations above the mean. P(20.03 less than X less than 20.08) =P(-1 less than Z less than 1.5) =0.3413+0.4332 =0.7745 So the probability is 0.7745.