A study of organized hiking groups to Grand Canyon National Park in the 1980s concluded that 15% of all group leaders were college-aged (under 23 years old). Suppose a random sample of 80 group leaders is taken.
a. Did the study treat age as a quantitative or a categorical variable?
b. The number X of group leaders in the sample who are college-aged has mean = 12 and standard deviation 3.2, and the distribution is approximately normal because np = 80(0.15) 12 and n(1 p)= 80(0.85) = 68 are both at least 10. Use the 68-95-99.7 Rule to sketch the distribution of X.
c. Is it likely that fewer than 20 of the 80 group leaders are college-aged?
d. The proportion of group leaders in the sample who are college-aged has mean 0.15 and standard deviation 0.04, and the distribution is approximately normal because np = 80(0.15) = 12 and n(1 p)= 80(0.85) = 68 are both at least 10. Use the 68-95-99.7 Rule to sketch the distribution of .
e. Is it likely that the sample proportion of group leaders who are college-aged is less than 0.05?