Pregunta
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.
© BFW Publishers per deciliter (
Ask by Lynch Crawford. in the United States
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The probability of the difference in sample means being less than 0 mg/dl is approximately 0.0301.
Solución

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Como
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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