SOLUTION: In a certain small town, Comcast has 100000 subscribers. According to Census data, 40 percent of the subscribers are single parent households. A simple random sample of 400 househ

Question 1148747: In a certain small town, Comcast has 100000 subscribers. According to Census data, 40 percent of the subscribers are single parent households. A simple random sample of 400 households were selected for a survey. The percentage of single parent households in the sample will be around
40 give or take ___ or so.
Estimate the chance that between 35 percent and 45 percent of the households in the sample are single parent households. ___

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
standard error of the sample = square root(0.40 * (1-0.40)/400) = 0.0245
:
The percentage of single parent households in the sample will be around
40 give or take 0.0245 or so.
:
Since the sample size is greater than 30, we can use the normal distribution's z-tables
:
Probability (P) (0.35 < X < 0.45) = P(X < 0.45) - P(X < 0.35)
:
z-score(0.45) = (0.45 - 0.40)/0.0245 = 2.04
:
P(X < 0.45) = 0.9793
:
z-score(0.35) = (0.35 - 0.40)/0.0245 = -2.04
:
P(X < 0.35) = 0.0207
:
P(0.35 < X < 0.45) = 0.9793 - 0.0207 = 0.9586 is approximately 0.96 or 96%
:

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