USMLE Sample Test Questions Step 1- 2024-16

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I am going to answer the sample USMLE Step 1 Questions with Explanation. These questions are available at USMLE.org

Serum LDL-cholesterol concentrations are measured in blood samples collected from 25 healthy volunteers. The data follow a normal distribution. The mean and standard deviation for this group are 130 mg/dL and 25 mg/dL, respectively. The standard error of the mean is 5.0. With a 95% confidence level, the true mean for the population from which this sample was drawn falls within which of the following ranges (in mg/dL)?

(A) 105-155

(B) 120-140

(C) 125-135

(D) 128-132

(E) 129-131

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Answer

To find the range for the true mean LDL cholesterol level in the population:

  1. Start with the sample mean of 130 mg/dL.
  2. Use the standard error (SEM) of 5.0 mg/dL.
  3. Multiply the SEM by 1.96 (for 95% confidence):
    1.96×5=9.8
  4. Add and subtract this margin (9.8) from the sample mean:
    • Lower limit: 130−9.8=120
    • Upper limit: 130+9.8=139

So, the 95% confidence range is 120 to 140 mg/dL.

The correct answer is B

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2 thoughts on “USMLE Sample Test Questions Step 1- 2024-16”

  1. Hi Dr. Adaba,

    The value 1.96 is a critical value from the Z-distribution (also known as the standard normal distribution) and corresponds to a confidence level of 95%. Here’s how it works:

    Confidence Level: When we say we’re using a 95% confidence level, we mean that we are 95% confident that the true population parameter (in this case, the population mean LDL cholesterol) lies within a specified range based on our sample data.

    Z-score: A Z-score represents the number of standard deviations a data point is from the mean. In the context of a normal distribution:

    For a 95% confidence interval, we want to include the middle 95% of the distribution.
    The remaining 5% of the distribution is divided equally into the two tails, with 2.5% in each tail (since 100% – 95% = 5%, and 5% ÷ 2 = 2.5% for each tail).
    The Z-score of 1.96 corresponds to the point that leaves 2.5% in the upper tail and 2.5% in the lower tail of the standard normal distribution.
    In simpler terms, a Z-score of 1.96 represents the value where 95% of the data lies between -1.96 and +1.96 standard deviations from the mean. This is why, for a 95% confidence level, we multiply the standard error by 1.96 to determine how far from the sample mean the true population mean is likely to be.
    Please let me know if you have any other questions.
    Thank you

  2. Please how did you get 1.96?

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