Question

1. Find the mean and standard deviation of the following binomial distribution: A company makes 800 sports bikes a month. 90% pass final inspection (and 10% fail and need to be fixed).

Answer 1

(a) Step1: The calculation of mean and standard deviation of Binomial distribution: The number of sports bikes pass final inspection in a month follows abinomial distribution with parameters n = = 800, and p = 0.90 q=1-p = 1-0.90 = 0.10 a = 0.10 Step 2: Let X be the random variable follows a binomi al distribution. X -B(n = 800, p = 0.90) The pmf of binomial distribution is P(X = x) = P(x) p*q*-*; x = 0,1,2,... 0 otherwise Step3: The mean number of sports bikes pass final inspection in a month is The formula for calculating the mean is 4= np 800(0.90) 720 4 = 720 Therefore, the value of mean number of sports bikes pass final inspection in a month is 4 = 1720 Step4: The formula for calculating the standard devation is J = npa =800(0.90) (0.10) = 800(0.90) (0.10) =72 8.485281 8.485281 Therefore, the standard deviation is on 8.485281 Therefore, the mean and standard deviation for the number of sports bikes pass final inspection in a month is 4 = 720 and us 8.4853