Suppose that 53% of all cars on interstate highways have one occupant (the drive

Question

Suppose that 53% of all cars on interstate highways have one occupant (the driver). Assume repeated random samples of 400 cars are examined, and a sample proportion of one-occupant cars is calculated for each sample. a) What will the mean of the sample proportions be? (percent form) b) What will the standard deviation of the sample proportions be? (percent form) c) Use the Empirical Rule to find the interval in which the sample proportions will fall 95% of the time. (percent form) Suppose that the actual mean Wechsler IQ score is 110 and the standard deviation is 24. Using Table 8.1: a) Find the probability that a person selected at random has an IQ score below 116. b) Find the probability that the mean IQ score for a sample of 36 people is below 116. c) What is the standard deviation of the sample mean IQ score for a sample of size 36?

Explanation / Answer

(1) (a) The mean of the distribution of sample proportions is equal to the population proportion = 53%

(b) of the sampling distribution of proportions = (p(1 - p)/n = (0.53 * 0.47/400) = 0.025

(c) z- score = ± 1.96

p1 = p + z * (p(1 - p)/n = 0.53 - 1.96 * 0.025 = 0.481

p2 = p + z * p(1 - p)/n = 0.53 + 1.96 * 0.025 = 0.579

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