Legs for a wooden dining room table are produced by a computer numerically controlled (CNC) lathe. The cutting blade lasts a mean time of 550 h with a standard deviation of 20 h. To avoid cutting errors, the shop manager would like to keep the probability of a failure to less than 0.002. How many hours should the blade be used before replacement? Explain.

A normal population has a mean of 75 and a standard deviation of 5, if you select a sample of 40, compute the probability that the sample mean is less than 74.

A fair die is rolled 8 times.

a. What is the probability that a die comes up 6 exactly twice?

b. What is the probability that the die comes up an odd number exactly five times?

c. Find the mean number of times a 6 comes up.

d. Find the mean number times an odd number comes up.

e. Find the standard deviation of times a 6 comes up.

f. Find the standard deviation of the number of times an odd number comes up.  

(1) Suppose IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability a random sample of 1200 people has a mean IQ of less than 99?

Suppose IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability a random sample of 150 people has a mean IQ between 102 and 103?

Suppose IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability a random sample of 100 people has a mean IQ of more than 104?