Pregunta
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The level of cholesterol in the blood for all men aged 20 to 34 follows a Normal distribution when mean milligrams
© BFW Publishers per deciliter ( ) and standard deviation . For 14 -year-old boys, blood cholesterol levels follow a Normal distribution with mean and standard deviation . Suppose we select independent SRSs of 25 men aged 20 to 34 and 36 boys aged 14 and calculate the sample mean cholesterol levels and .
What is the probability of getting a difference in sample means that’s less than ?
Round to 4 decimal places.

Ask by Lynch Crawford. in the United States
Jan 23,2025

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The probability of the difference in sample means being less than 0 mg/dl is approximately 0.0301.

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The Deep Dive

To find the probability of , we first need to calculate the distributions of the sample means. For the men, the mean is mg/dl and the standard error (SE) of the sample mean is mg/dl. For the boys, the mean is mg/dl and the SE is mg/dl.
Next, we find the mean and standard deviation of the difference in sample means:
Now, we standardize the difference to find the Z-score for 0:
Using standard normal distribution tables or calculators, we find the probability corresponding to .
This gives us:
Thus, the probability of getting a difference in sample means is approximately 0.0301 when rounded to four decimal places.

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