g Students conducted a survey and found out that 36% of their peers on campus had tattoos but only 4% of their peers were smokers. If 100 students were surveyed, can these students use the Normal approximation to construct a confidence interval for the proportion of students in the population who are smokers? No, because either n p np or n (1 - p) n (1-p) are greater than 15. Yes, because both n p np and n (1 - p) n (1-p) are greater than 15. Yes, because both n p np and n (1 - p) n (1-p) are less than 15. No, because either n p np or n (1 - p) n (1-p) are less than 15.

Question

Mathematics

Giselle Sutton

1 June, 14:50

g Students conducted a survey and found out that 36% of their peers on campus had tattoos but only 4% of their peers were smokers. If 100 students were surveyed, can these students use the Normal approximation to construct a confidence interval for the proportion of students in the population who are smokers? No, because either n p np or n (1 - p) n (1-p) are greater than 15. Yes, because both n p np and n (1 - p) n (1-p) are greater than 15. Yes, because both n p np and n (1 - p) n (1-p) are less than 15. No, because either n p np or n (1 - p) n (1-p) are less than 15.

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Jadon · Answer 1

D) No, because either np or n (1-p) are less than 15.

Step-by-step explanation:

Percentage of students who had tattoos = 36%

Percentage of students who were smokers = 4%

Sample size = n = 100

The condition to use the Normal distribution as an approximation to construct the confidence interval for population proportion is:

Both np and n (1-p) must be equal to or greater than 15.

Since, we are interested in smokers only, so p = 4% = 0.04

np = 100 x 0.04 = 4

n (1 - p) = 100 x 0.96 = 96

Since, np < 15, we cannot use the Normal distribution as an approximation here.

Therefore, the correct answer is:

No, because either np or n (1-p) are less than 15.