Normal Distribution and Binomial Distribution Analysis

Extract

[...] X follows a normal distribution N(1200,200). Using a calculator, we find : The probability that a lamp works at least 1600 hours is 2.28%. The probability that a lamp functions at least 1600 hours is approximately 14.66%. Exercise Let X be the random variable that associates a lamp with its diameter in mm. X follows a normal distribution with a mean of 20 and a standard deviation of 0.05. Let Y be the random variable that associates a washer with its diameter in mm. [...]

[...] X follows the binomial distribution with parameters n = 10 and p = 0.62. The probability that he crosses between 4 and 6 zombies is about 47%. On average, he crosses 6 zombies. Exercise The sample size is 36." The average is approximately 148 cm. The variance is approximately equal to 7.15². There is a 95% chance that the mean of the population lies in the interval [145 We assume the population standard deviation is equal to the sample standard deviation. [...]

[...] Y follows a normal distribution with a mean of 20 and a standard deviation of 0.07. X and Y follow normal distributions and are independent, so Y - X follows a normal distribution with mean - i.e and variance + i.e.: Y-X follows a normal law with expectation 0 and standard deviation 0.086 The probability that the peg and the hole cannot fit together is therefore 1/2. Let X be the random variable that associates with a peg its diameter in mm. [...]