1. The number of acres burned by forest and range fires each year in western New Mexico is normally distributed with a mean of 4,300 acres. Last year 4,600 acres burned and it was reported that this acreage was 1/2 standard deviation above the mean. What is the standard deviation of acres burned per year?
2. The number of acres burned by forest and range fires each year in western Nevada is normally distributed with a mean of 5,300 acres. Last year 4,400 acres burned and it was reported that this acreage was 1.43 standard deviations below the mean. What is the standard
deviation of acres burned per year?
3. The Squinta Theater chain conducted a study to determine the amount spent by patrons per visit at theater concessions. They found the distribution of concession expenditures to be normally distributed with a mean of $4.11 and a standard deviation of $1.17.
a. How likely is it that a randomly selected customer will have spent between $4.11 and $6.00?
b. How likely is it that a randomly selected customer will have spent more than $6.00?
c. What is the probability that the next customer will spend at least $2.00?
4. A machining process produces specialty metal parts used in aircraft. A particular part is designed to be 62 cm in length. The machine is set to cut at 62 cm but the process is stochastic with a mean length of 62 cm and a standard deviation of 0.04 cm. It is know that the process follows a normal distribution.
a. The acceptable tolerances for the part are 62 cm plus or minus 0.10 cm. What proportion of parts cut by this machine is within the specified tolerances?
b. If the standard deviation were 0.03 cm, what proportion of parts cut by this machine is within the specified tolerances?
5. Assume pretzel sales at Temple football games are normally distributed with a mean of 1216 and a standard deviation of 236.
a. If the concession manager orders 1500 pretzels for the game next week, what is the probability that they will sell out?
b. If the concession manager wants to sell out of pretzels no more than 20% of the time, what should his pretzel order be?