At a certain concert, 43% of the audience was under 20 years old. A random sample of n = 181 members of the audience was selected. Find the value of sample mean, the mean of the distribution of sample proportions.
Write only a number as your answer. Do not write as a percentage.
To find the value of the sample mean, the mean of the distribution of sample proportions, we need to use the formula:
Sample Mean = Population Proportion
In this case, the population proportion is 43% or 0.43 since it is given that 43% of the audience was under 20 years old.
Therefore, the value of the sample mean is 0.43.
The sample mean of the distribution of sample proportions can be found using the formula:
Sample Mean = Proportion * Total
In this case, the proportion is 43% (or 0.43) and the total is the sample size, n = 181.
Sample Mean = 0.43 * 181 = 77.83
Therefore, the value of the sample mean (mean of the distribution of sample proportions) is approximately 77.83.