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An article reported that in a large study carried out in the state of New York, approximately 60% of the study subjects lived within 1 mile of a hazardous waste site. Let p denote the proportion of all New York residents who live within 1 mile of such a site, and suppose that = 0.6. (a) Would > based on a random sample of only 10 residents have approximately a normal distribution? Explain why or why not. O Yes, because np < 10 and n(1-p) < 10. OYes, because np > 10 and n(1-P) > 10. O No, because np < 10. O No, because np > 10. (b) What are the mean value and standard deviation of p based on a random sample of size 390? (Round your standard deviation to four decimal places.) mean standard deviation (c) When n = 390, what is P(0.55 ≤ ≤ 0.65)?

An article reported that in a large study carried out in the state of New York, approximately 60% of the study subjects lived within 1 mile of a hazardous waste site. Let p denote the proportion of all New York residents who live within 1 mile of such a site, and suppose that = 0.6. (a) Would > based on a random sample of only 10 residents have approximately a normal distribution? Explain why or why not. O Yes, because np < 10 and n(1-p) < 10. OYes, because np > 10 and n(1-P) > 10. O No, because np < 10. O No, because np > 10. (b) What are the mean value and standard deviation of p based on a random sample of size 390? (Round your standard deviation to four decimal places.) mean standard deviation (c) When n = 390, what is P(0.55 ≤ ≤ 0.65)?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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An article reported that in a large study carried out in the state of New York, approximately 60% of the study subjects lived within 1 mile of a hazardous waste site. Let p denote the proportion of all New York residents who live within 1 mile of such a site, and suppose that p 0.6. (a) Would p based on a random sample of only 10 residents have approximately a normal distribution? Explain why or why not. Yes, because np < 10 and n(1 − p) < 10. Yes, because np > 10 and n(1 − p) > 10. No, because np < 10. No, because np > 10. (b) What are the mean value and standard deviation of p based on a random sample of size 390? (Round your standard deviation to four decimal places.) mean standard deviation (c) When n = 390, what is P(0.55 ≤ ≤ 0.65)? (d) Is the probability calculated in Part (c) larger or smaller than would be the case if n = 490? Answer without actually calculating this probability. The probability from Part (c) is larger because as n increases, the standard deviation of increases. The probability from Part (c) is larger because as n increases, the standard deviation of ô decreases. The probability from Part (c) is smaller because as n increases, the standard deviation of p decreases. The probability from Part (c) is smaller because as n increases, the standard deviation of p increases.
Transcribed Image Text:An article reported that in a large study carried out in the state of New York, approximately 60% of the study subjects lived within 1 mile of a hazardous waste site. Let p denote the proportion of all New York residents who live within 1 mile of such a site, and suppose that p 0.6. (a) Would p based on a random sample of only 10 residents have approximately a normal distribution? Explain why or why not. Yes, because np < 10 and n(1 − p) < 10. Yes, because np > 10 and n(1 − p) > 10. No, because np < 10. No, because np > 10. (b) What are the mean value and standard deviation of p based on a random sample of size 390? (Round your standard deviation to four decimal places.) mean standard deviation (c) When n = 390, what is P(0.55 ≤ ≤ 0.65)? (d) Is the probability calculated in Part (c) larger or smaller than would be the case if n = 490? Answer without actually calculating this probability. The probability from Part (c) is larger because as n increases, the standard deviation of increases. The probability from Part (c) is larger because as n increases, the standard deviation of ô decreases. The probability from Part (c) is smaller because as n increases, the standard deviation of p decreases. The probability from Part (c) is smaller because as n increases, the standard deviation of p increases.
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