Respuesta :
Answer:
Mean and standard deviation of the sampling distribution of the sample proportions are 76 and 0.0427 respectively.
Step-by-step explanation:
The mean for a sample proportion is given by μ = np
n = sample size = 100
p = fraction of the sample proportion that have what is being tested = 76% = 0.76
μ = 0.76 × 100 = 76.
Standard deviation of a sample proportion = σ = √[p(1-p)/n] = √(0.76×0.24/100) = 0.0427
Answer:
Mean = 76
Standard deviation = 0.043
Step-by-step explanation:
We are given that in a large population, 76% of the households own microwaves. Also, a simple random sample of 100 households is to be contacted and the sample proportion computed.
The above situation can be represented as a Binomial distribution where;
Let X = Proportion of households who own microwaves, i.e;
X ~ [tex]Binom(n=100,p=0.76)[/tex]
Here, n = sample size
p = probability of success
So, the mean of the sampling distribution of the sample proportions is given by, [tex]\mu[/tex] = n * p = 100 * 0.76 = 76 .
Standard deviation of the sampling distribution of the sample proportions, σ = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex] = [tex]\sqrt{\frac{0.76(1-0.76)}{100} }[/tex] = 0.043 .
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