Binomial Distribution, Variance, & Standard Deviation

5% of electric light bulbs are defective at manufacture. 6 bulbs are randomly tested, with each one being replaced before the next is chosen. Determine the probability that two bulbs are defective.

5% of electric light bulbs are defective at manufacture. 6 bulbs are randomly tested, with each one being replaced before the next is chosen. Determine the probability that at least one bulb is defective.

Records show that 6% of the items assembled on a production line are faulty. A random sample of 12 items is selected with replacement. Find the probability that none will be faulty.

Records show that 6% of the items assembled on a production line are faulty. A random sample of 12 items is selected with replacement. Find the probability that at most one will be faulty.

Records show that 6% of the items assembled on a production line are faulty. A random sample of 12 items is selected with replacement. Find the probability that at least two will be faulty.

Records show that 6% of the items assembled on a production line are faulty. A random sample of 12 items is selected with replacement. Find the probability that less than four will be faulty.

A coin is tossed 10 times and X is the number of heads which occur. Find the mean of X.

A coin is tossed 10 times and X is the number of heads which occur. Find the variance of X.

A coin is tossed 10 times and X is the number of heads which occur. Find the standard deviation of X.

Bolts produced by a machine vary in quality. The probability that a given bolt is defective is 0.04. Random samples of 30 bolts are taken from the week's production.

If X is the number of defective bolts in a sample, find the mean.