5% of batteries produced at a factory are defective. Use the binomial model to find the probability that 1 battery in a pack of 16 is defective.
P(x) = [n! / (x!(n-x)!)] * p^x * q^(n-x)
P(x) = [16! / (1!(16-1)!)] * (0.05)^1 * (0.95)^(16-1)
P(x) = [16! / (1!15!)] * (0.05) * (0.95)^15
P(x) = (16 * (15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)/(1*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)) * (0.05) * (0.95)^15
P(x) = 16 * (0.05) * (0.95)^15
P(x) = 0.0000031728 (rounded to 8 decimal places)
The probability that 1 battery in a pack of 16 is defective is approximately 0.0000031728.