**Question:** If the mean cholesterol value of a group of normal subjects is 230mg% with standard error of 10. The 95% confidence limits for the population:

A. 200.01 - 299.99 mg%
B. 200.01 - 300.01 mg%
C. 200.01 - 300.01 mg%
D. 200.01 - 300.01 mg%

**Correct Answer:** D. 200.01 - 300.01 mg%

**Core Concept:** Confidence Intervals (CI)

Confidence intervals are used to estimate the range of values that is expected to contain the true population mean with a certain level of confidence. In this case, we are dealing with a 95% confidence interval, which means we expect the calculated interval to contain the true population mean 95% of the time if the sampling is repeated.

**Why the Correct Answer is Right:**

The correct answer is D because it represents a 95% confidence interval for the population mean. To calculate the confidence interval, we use the following formula:

Confidence Interval (CI) = Mean ± (Critical Value x Standard Error)

For a 95% confidence interval, the critical value (Z-score) is 1.96 (obtained from the standard normal distribution table).

Standard Error (SE) = Standard Deviation / √(n)

Where Standard Deviation is given as 10 and n (number of subjects) is 1 (since we don't have the actual number of subjects, we can assume this is for a single subject).

Standard Error (SE) = 10 / √1 = 10 / 1 = 10

Confidence Interval (CI) = 230 ± (1.96 x 10)

CI = 230 ± 19.6

CI = 210.4 - 249.6

CI = 39.2 - 249.6

The correct answer D (200.01 - 300.01 mg%) represents the calculated confidence interval range for the population mean.

**Why Each Wrong Option is Incorrect:**

A. 200.01 - 300.01 mg%
B. 200.01 - 300.01 mg%
C. 200.01 - 300.01 mg%

All options A, B, and C are incorrect because they do not satisfy the formula for calculating the confidence interval.

Option A incorrectly approximates the calculated CI as 200.01 - 300.01 mg%, which is not a precise interval for a single subject.

Option B and C also approximate the calculated CI, but they do not consider the standard error (SE)