There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 67. There are 30 red marbles in the bag and each is equally likely to be chosen. Work out how many marbles in total there must be.

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.