1. Suppose the age that children learn to walk is normally distributed with a mean of 13 months and a standard deviation of 2.4 months. 34 randomly selected people were asked at what age they learned to walk. Round all answers to 4 decimal places where possible.

a. What is the distribution of XX? XX ~ N(__,__)

b. What is the distribution of xx? xx ~ N(___,___)

c. What is the probability that one randomly selected person learned to walk when the person was between 12.5 and 13.5 months old? _____

d. For the 34 people, find the probability that the average age that they learned to walk is between 12.5 and 13.5 months old.?______

e. For part d), is the assumption that the distribution is normal necessary? No? Yes?

f. Find the IQR for the average first-time walking age for groups of 34 people. Q1 = ___ months Q3 = ____ months IQR:____ months

2. The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.4 ppm and standard deviation 1.4 ppm. 7 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.

a. What is the distribution of XX? XX ~ N(___,____)

b. What is the distribution of xx? xx ~ N(___,____)

c. What is the probability that one randomly selected city's waterway will have less than 9.5 ppm pollutants?

d. For the 7 cities, find the probability that the average amount of pollutants is less than 9.5 ppm. _____?

e. For part d), is the assumption that the distribution is normal necessary? YesNo

f. Find the IQR for the average of 7 cities. Q1 = ____ ppm Q3 =_____ ppm IQR: _____ ppm

3. The lengths of adult males' hands are normally distributed with a mean of 185 mm and a standard deviation is 7.3 mm. Suppose that 45 individuals are randomly chosen. Round all answers to 4 where possible.

a. What is the distribution of xx? xx ~ N(____,____)

b. For the group of 45, find the probability that the average hand length is more than 184.?____

c. Find the first quartile for the average adult male hand length for this sample size. ?____

d. For part b), is the assumption that the distribution is normal necessary? Yes? or No?