An SRS of 50 students was selected from a population of 200 students. The population has a parameter equal to 0.85. What is the center and spread of the sampling distribution?

A. [tex]\mu_{\rho} = 0.85, \sigma_{\rho} = 0.025[/tex]
B. [tex]\mu_{\rho} = 1.4 \times 0.85, \sigma_{p} = 0.05[/tex]
C. We cannot compute the center because it violates the large counts condition.
D. We cannot compute the spread because it violates the 10% condition.
E. We cannot compute the center or spread because both the large counts condition and 10% condition are violated.

Question

11-12-2024
Mathematics

High School

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An SRS of 50 students was selected from a population of 200 students. The population has a parameter equal to 0.85. What is the center and spread of the sampling distribution?

A. [tex]\mu_{\rho} = 0.85, \sigma_{\rho} = 0.025[/tex]
B. [tex]\mu_{\rho} = 1.4 \times 0.85, \sigma_{p} = 0.05[/tex]
C. We cannot compute the center because it violates the large counts condition.
D. We cannot compute the spread because it violates the 10% condition.
E. We cannot compute the center or spread because both the large counts condition and 10% condition are violated.

Answer :

Final answer:

In a simple random sample (SRS) of 50 students, the mean of the sampling distribution is 0.85, which is equal to the population parameter. The standard deviation, or spread, is calculated to be around 0.05 using the statistical formula for standard deviation.

Explanation:

Here in this question, we're working with the concept of the sampling distribution. For any sampling distribution, its center, or mean, would always be equal to the population parameter. So, in this case, our μrho, the mean of the population, is 0.85. This comes from the parameter given, which is 0.85.

Next, we calculate the spread or standard deviation (σrho) of the distribution using the formula: √((p(1-p))/n), where: p is the parameter and n is the number of observations. Here, p = 0.85 and n = 50, giving us √((0.85(1-0.85))/50) = √(0.1275/50) = √0.00255 ~ 0.05. Thus, the center (mean) of the sampling distribution is 0.85 and the spread (standard deviation) is 0.05.

Therefore, the answer to the question is (B) μrho=0.85 , σrho=0.05.

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Answer :

Final answer:

Explanation:

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