Answer:
Given : Students conducted a survey and found out that 36% of their peers on campus had tattoos, but only 4% of their peers were smokers.
To Find : If 100 students were surveyed, can these students use the Normal approximation to study the proportion of students in the population who have tattoos?
Solution:
Peers had tattoos = 36% = 0.36
So, p = 0.36
Condition for normal approximation: [tex]np\geq10[/tex] and [tex]n(1-p)\geq 10[/tex]
We are given that total students = 100
So, n = 100
Now substitute the values in the condition
[tex]np\geq10[/tex] and [tex]n(1-p)\geq10[/tex]
[tex]100 \times 0.36 \geq10[/tex] and [tex]100(1-0.36\geq 10[/tex]
[tex]36 \geq10[/tex] and [tex]100(0.64)\geq 10[/tex]
[tex]36 \geq 10[/tex] and [tex]64\geq 10[/tex]
Since the conditions are satisfied
Hence we can use Normal approximation to study the proportion of students in the population who have tattoos
