SOLUTION: z is the standard normal random variable (with a mean 0 and standard deviation 1), and X is a normal random variable with mean and standard deviation. a machine produced bolts

Question 435584: z is the standard normal random variable (with a mean 0 and standard deviation 1), and X is a normal random variable with mean and standard deviation.
a machine produced bolts with a mean diameter of 0.30 inches and a standard deviation of 0.01 inches. The diameters are approximately noramlly distributes. What is the probability that a randomly selected bolt will have a diameter greater than 0.32 inches.
(a) What is the probability that a randomly selected bolt has diameter greater than 0.32 inches?
b) In a box of 100 such bolts, how many do you expect to have a diameter greater than 0.32?

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
(a) 0.32 inches is 2 standard deviations above the mean. Hence by the Empirical rule, 95% of the distribution is between [0.28, 0.32], or 2.5% would be greater than 0.32 inches, or a probability of 0.025.
(b) 100* 0.025 = 2.5 bolts.
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