1)
The inside diameter of a randomly selected piston ringis a random variable with mean value 11 cm and standard deviation0.02 cm. Suppose the distribution of the diameter is normal. (Roundyour answers to four decimal places.)
(a) Calculate P(10.99 ? X ? 11.01) when n =16.
(b) How likely is it that the samplemean diameter exceeds 11.01 when n =25?
2)
Suppose the sediment density (g/cm) of a randomlyselected specimen from a certain region is normally distributedwith mean 2.7 and standard deviation0.85.
(a) If a random sample of 25 specimensis selected, what is the probability that the sample averagesediment density is at most 3.00? Between 2.7 and 3.00? (Round your answers to four decimalplaces.)
at most 3.00 = ?
between 2.7 and 3.00 =?
(b) How large a sample size would berequired to ensure that the probability in part (a) is at least0.99? (Round your answer up to the nearest whole number.)
3)
The inside diameter of a randomly selected piston ringis a random variable with mean value 10 cmand standard deviation 0.05cm.
(a) If X isthe sample mean diameter for a random sample of n = 16rings, where is the sampling distribution of
X centered andwhat is the standard deviation of the
Xdistribution? (Enter your standard deviation to five decimalplaces.)
center = ?
standard deviation = ?
(b) Answer the questions posed in part (a)for a sample size of n = 64 rings. (Enter your standarddeviation to five decimal places.)
center = ?
standard deviation = ?
