Question

ch 22 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 study the proportion of students in the population who have tattoos? (note: np is the number of successes, n(1 - p) is the number of failures.)

yes, because both np and n(1 - p) are less than 15.

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

no, because either np or n(1 - p) are greater than 15.

yes, because both np and n(1 - p) are greater than 15.

Explanation:

Step1: Calculate \(np\)

Given \(n = 100\) and \(p=0.36\), then \(np=100\times0.36 = 36\)

Step2: Calculate \(n(1 - p)\)

\(n(1 - p)=100\times(1 - 0.36)=100\times0.64 = 64\)

Step3: Check the conditions for normal approximation

For normal approximation to the binomial (to study the proportion), we need \(np\geq15\) and \(n(1 - p)\geq15\). Here \(np = 36\geq15\) and \(n(1 - p)=64\geq15\)

Answer:

Yes, because both \(np\) and \(n(1 - p)\) are greater than \(15\).