The proportion of a population under the age of 18 is known to equal 0.42 (42%). a) Determine the probability the proportion of 100 randomly selected members of the population will be within 0.04 of the actual population proportion, i.e., ?(0.38 < ? < 0.46) b) Determine the probability the proportion of 500 randomly selected members of the population will be within 0.04 of the actual population proportion. c) Does this ensure the proportion for a larger sample of a population will be within closer to the population proportion than the proportion for a smaller sample? Explain your reasoning.
The proportion of a population under the age of 18 is known to equal 0.42 (42%). a) Determine the probability the proportion of 100 randomly selected members of the population will be within 0.04 of the actual population proportion, i.e., ?(0.38 < ? < 0.46) b) Determine the probability the proportion of 500 randomly selected members of the population will be within 0.04 of the actual population proportion. c) Does this ensure the proportion for a larger sample of a population will be within closer to the population proportion than the proportion for a smaller sample? Explain your reasoning.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter7: Percents
Section7.1: Percents And Fractions
Problem 33E
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The proportion of a population under the age of 18 is known to equal 0.42 (42%).
a) Determine the
within 0.04 of the actual population proportion, i.e., ?(0.38 < ? < 0.46)
b) Determine the probability the proportion of 500 randomly selected members of the population will be
within 0.04 of the actual population proportion.
c) Does this ensure the proportion for a larger sample of a population will be within closer to the
population proportion than the proportion for a smaller sample? Explain your reasoning.
Please include any formulas used and detalied explenation.
Transcribed Image Text:The proportion of a population under the age of 18 is known to equal 0.42 (42%).
a) Determine the probability the proportion of 100 randomly selected members of the population will be
within 0.04 of the actual population proportion, i.e., P(0.38 <p <0.46)
b) Determine the probability the proportion of 500 randomly selected members of the population will be
within 0.04 of the actual population proportion.
c) Does this ensure the proportion for a larger sample of a population will be within closer to the
population proportion than the proportion for a smaller sample? Explain your reasoning.
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VIEWStep 2: Determine the probability the proportion of n=100 of the population will be within 0.04 of p:
VIEWStep 3: Determine the probability the proportion of n=500 of the population will be within 0.04 of p:
VIEWStep 4: Explain your reasoning for part (c):
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