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1)Use the normal approximation to the binomial to find the probabilities for the specific values of X: n = 30, p = 0

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1)Use the normal approximation to the binomial to find the probabilities for the specific values of X:

1. n = 30, p = 0.5, X = 18

2. n = 50, p = 0.8, X = 44

3. n = 100, p = 0.1, X = 12

2. Home Ownership  In a recent year, the rate of US home ownership was 65.9%.  Choose a random sample of 120 households across the US.  What is the probability that 65 to 85 (inclusive) of the live in homes that they own?

n = 120, p = 0.659, q = 0.341

 

3. Playing Video Games  In a recent study of 35 ninth-grade students, the mean number of hours per week that they played video games was 16.6.  The standard deviation of the population was 2.8.

1. Find the best point estimate of the population mean
2. Find the 95% confidence interval of the mean of the time playing video games
3. Find the 99% confidence integral of the mean of the time playing video games
4. Which is larger?  Explain why

4. Distance Traveled to Work  A recent study of 28 randomly selected employees of a company showed that the mean of the distance they traveled to work was 14.3 miles.  The standard deviation of the sample was 2.0 miles.  Find the 95% confidence interval of the true mean.  If a manager wanted to be sure that most of his employees would not be late, how much time would he suggest they allow for the commute if the average speed were 30 miles per hour?

5. Chicago Commuters  A sample of 14 randomly selected commuters in Chicago showed the average of the commuting times was 33.2 minutes.  If the standard deviation was 8.3 minutes, find the 95% confidence interval of the true mean.