Question

Concerns about climate change and CO reduction have initiated the commercial production of blends of biodiesel (e.g., fromrenewable sources) and petrodiesel (from fossil fuel). Random samples of 48 blended fuels are tested in a lab to ascertain the bio/totalcarbon ratio.(a) If the true mean is .9200 with a standard deviation of 0.0050, within what interval will 68 percent of the sample means fall? (Roundyour answers to 4 decimal places.)

Answer 1

(0.9193, 0.9207)

Step-by-step explanation:

The interval for the sample mean can be calculated as

`x-z(s)/(√(n))\leq x^(\prime)\leq x+z(s)/(√(n))`

Where x is the mean, s is the standard deviation, n is the size of the sample, and z is the standard value for the 68%, so using the standard normal table, we get that z = 1.

Replacing x = 0.92, s = 0.0050, n = 48 and z = 1, we get:

`\begin{gathered} 0.92-1(0.0050)/(√(48))\leq x^(\prime)\leq0.92+1(0.0050)/(√(48)) \\ \\ 0.92-0.0007\leq x^(\prime)\leq0.92+0.0007 \\ 0.9193\leq x^(\prime)\leq0.9207 \end{gathered}`

Therefore, the interval is

(0.9193, 0.9207)