Students conducted a survey and found out that 36 of their p

Students conducted a survey and found out that 36% of their peers on campus had tattoos, but only 4% of their peers were smokers

A) If 200 students were surveyed, can these students use the Normal approximation to study the proportion of students in the population who have tattoos?

B) If 200 students were surveyed, can these students use the Normal approximation to study the proportion of students in the population who are smokers?

Solution

a)

For tattoos, p = 0.36, q = 0.64. Thus, as n = 200,

np = 72 > 10
nq = 128 > 10

As they are both greater than 10, then the normal approximation can be used.

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b)

For smokers, p = 0.04, q = 0.96. Thus, as n = 200,

np = 8 < 10
nq = 192 > 10

As np is not greater than 10, then the normal approximation CANNOT be used.