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14#A corporation that maintains a large fleet of company cars for the use of its sales staff is interested in the mean distance driven monthly per salesperson. The following list gives the monthly distances in miles driven by a random sample of 11 salespeople.2482, 2300, 2640, 2085, 2425, 1851, 2346, 1876, 2444, 2153, 2290Send data to calculatorBased on this sample, find a 95% confidence interval for the mean number of miles driven monthly by members of the sales staff, assuming that monthly driving distances are normally distributed. Give the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.

Respuesta :

Solution

Given the data set 2482, 2300, 2640, 2085, 2425, 1851, 2346, 1876, 2444, 2153, 2290

The confidence interval formula is

Calculate the standard deviation of the data

The standard deviation is

237.67

Calculate the sample mean

The mean is 2262.91

[tex]\begin{gathered} s=237.67 \\ n=11 \\ mean=2262.909 \\ z=1.96 \end{gathered}[/tex][tex]\begin{gathered} CI=2262.909\pm1.96(\frac{237.67}{\sqrt{11}}) \\ CI=2262.909\pm1.96(71.6602) \\ CI=2262.909\pm140.453992 \\ CI\text{ = 2122.455008 to 2403.362992 to} \end{gathered}[/tex]

Thus, the lower limit is

2122.455 ( 3 decimal places)

The Higher limit is 2403.363 ( 3 decimal places)

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