A study of hikers in Grand Canyon National Park in the 1980s concluded that 30% of all hikers express a preference for lessdeveloped areas. Suppose a random sample of 84 hikers is taken.
a. The number X of hikers in the sample who prefer less-developed areas has mean 25.2 and standard deviation 4.6, and the distribution is approximately normal because np = 84(0.3) = 25.2 and n(1 p)= 84(0.7) = 58.8 are both at least 10. Use the 68-95-99.7 Rule to sketch the distribution of X.
b. Is it likely that at least 40 of the 84 hikers prefer less-developed areas? Explain.
c. The proportion of hikers in the sample who prefer less-developed areas has mean
0.3 and standard deviation 0.05, and the distribution is approximately normal because np = 84(0.3) = 25.2 and n(1 p) = 84(0.7) = 58.8 are both at least 10. Use the 68-95-99.7 Rule to sketch the distribution of .
d. Is it likely that the sample proportion of hikers preferring less-developed areas is at least 0.2? Explain. *7