Asked by Rachel Weatherbee on Jun 19, 2024
Verified
A sA sample of 51 observations will be taken from an infinite population.The population proportion equals 0.85.The probability that the sample proportion will be between 0.8327 and 0.8631 is
A) 0.9998.
B) 0.0002.
C) 0.2387.
D) 0.7613.
Sample Proportion
The fraction or percentage of sample observations that belongs to a particular category or possesses a particular attribute.
Population Proportion
The proportion or percentage of a specific characteristic within the entire population.
- Execute calculations of probabilities regarding estimates of means and proportions under the umbrella of inferential statistics.
Verified Answer
HE
Hazel Exo88Jun 21, 2024
Final Answer :
C
Explanation :
We can use the Central Limit Theorem as the sample size is sufficiently large (greater than 30).
The mean of the sample proportion will be 0.85 (same as population proportion), and the standard deviation of the sample proportion will be sqrt((0.85*(1-0.85))/51) ≈ 0.064.
Now we standardize the values:
Z1 = (0.8327 - 0.85)/0.064 ≈ -0.266
Z2 = (0.8631 - 0.85)/0.064 ≈ 0.204
Using a standard normal table, we find the probability of Z being between -0.266 and 0.204 is approximately 0.2387. Therefore, the answer is C) 0.2387.
The mean of the sample proportion will be 0.85 (same as population proportion), and the standard deviation of the sample proportion will be sqrt((0.85*(1-0.85))/51) ≈ 0.064.
Now we standardize the values:
Z1 = (0.8327 - 0.85)/0.064 ≈ -0.266
Z2 = (0.8631 - 0.85)/0.064 ≈ 0.204
Using a standard normal table, we find the probability of Z being between -0.266 and 0.204 is approximately 0.2387. Therefore, the answer is C) 0.2387.
Learning Objectives
- Execute calculations of probabilities regarding estimates of means and proportions under the umbrella of inferential statistics.
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