1. Mrs. Smith's reading class can read a mean of 175 words per minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a special award. What is the minimum number of words per minute a student would have to read in order to get the award?
2. The standard deviation of a distribution is 20. If a sample of 225 is selected, what is the standard error of the mean?
3. A survey of 250 lobster fishermen found that they catch an average of 32 pounds of lobster per day with a standard deviation of four pounds. If a random sample of 30 lobster fishermen is selected, what is the probability that their average catch is less than 31.5 pounds?
4. What is the z value such that 50% of the total area lies to the right of the curve in any normal distribution?
6. Find the probability P(z > 0.73) using the standard normal distribution.
8. Find the probability P(Z < 0.22) using the standard normal distribution.
9. For a normal curve with mean 8 and standard deviation 6, which of the following parts of the normal curve will have an area of approximately 34%?
12. Find the probability P(–0.62 < z < –0.01) using the standard normal distribution.
14. The mean weight of loads of rock is 43.0 tons with a standard deviation of 12.0 tons. If 9 loads are chosen at random for a weight check, find the probability that the mean weight of those loads is less than 38.60 tons. Assume that the variable is normally distributed.
15. Find the probability P(–1.04 < z < 1.11) using the standard normal distribution.