Question

At a certain concert, 73 % of the audience was under 20 years old. A random sample of n = 146 members of the audience was selected. Find the value of , the mean of the distribution of sample proportions.

Answer 1

Answer: p = 0.73

Explanation:

Given that,

73% of the audience was under 20 years old :

so, probability (p) = 0.73

n = 146

Mean of the distribution of sample proportion = ?

According to central limit theorem,

np(1-p) ≥ 10

146 × 0.73(0.27) ≥ 10

28.77 ≥ 10

∴ Central limit theorem assumes that the sample distribution of the sample proportion is normally distributed.

Hence, the mean of the distribution of sample proportion:

μ = p = 0.73