Assume that 32% of students at a university wear contact lenses.We randomly pick 300 students.Describe the sampling distribution model of the proportion of students in this group who wear contact lenses.
A)N(32%,1.3%)
B)N(32%,2.7%)
C)N(68%,2.7%)
D)Binom(300,32)
E)There is not enough information to describe the distribution.

Question

Quizplus · Accepted Answer

The sampling distribution of proportions follows a normal distribution if the sample size is large enough (n > 30) and the population proportion is not too close to 0 or 1. In this case, n = 300, which is large enough, and the population proportion is 0.32. The standard deviation of the sampling distribution of proportions is calculated as sqrt(p*(1-p)/n), which is approximately 0.027 or 2.7%. Therefore, the sampling distribution model of the proportion of students in this group who wear contact lenses is N(32%,2.7%).

Assume That 32% of Students at a University Wear Contact