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Concerns about climate change and CO2 reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 48 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. (a) If the true mean is .9050 with a standard deviation of 0.0100, within what interval will 90 percent of the sample means fall

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Answer:

(0.9036, 0.9064)

Step-by-step explanation:

Given that:

True mean (m) = 0.9050

Standard deviation (s) = 0.0100

Sample size ( n) = 48

Interval for 90% of the sample mean :

Mean ± Error

Error = Zcritical * (standard deviation /sqrt(n))

Zcritical at 90% confidence interval = 1.64

Hence,

Error = 1.64 * (0.0100/sqrt(48)) = 0.0014433

Lower boundary = m - Error = (0.9050 - 0.0014433) = 0.9035567

Upper boundary = m + Error = (0.9050 + 0.0014433) = 0.9064433

(0.9036, 0.9064)