Final answer:
Using the sample mean, standard deviation, and size provided, and the Z-score for a 90% confidence level, we calculated the 90% confidence interval for the mean BMI of young women to be 26.324 < μ < 27.276, which corresponds to Option B) 26.322 < μ < 27.277.
The correct option is B.
Step-by-step explanation:
The student is asking how to calculate a 90% confidence interval for the mean BMI of young women, using the sample mean of 26.8, sample standard deviation of 7.42, and a sample size of 654. To calculate the confidence interval, we use the formula for a confidence interval of a mean, which is:
μ = α +/- (Z*(σ/√n))
Where μ is the sample mean, Z is the Z-score associated with the confidence level (in this case, the Z-score for a 90% confidence interval is approximately 1.645), σ is the standard deviation, and n is the sample size. Plugging in the values we have:
26.8 +/- (1.645*(7.42/√654))
Calculating the margin of error:
1.645*(7.42/√654) ≈ 0.476
Now we can find the interval:
26.8 - 0.476 < μ < 26.8 + 0.476
So, the 90% confidence interval is:
26.324 < μ < 27.276
Therefore, the correct answer is Option B) 26.322 < μ < 27.277.
The correct option is B.