The distribution of a sample of the outside diameters of PVC pipes approximates a symmetrical, bell-shaped distribution. The arithmetic mean is 14.0 inches, and the standard deviation is 0.1 inches. About 68% of the outside diameters lie between what two amounts? a. 13.5 and 14.5 inchesb. 13.0 and 15.0 inchesc. 13.9 and 14.1 inchesd. 13.8 and 14.2 inches

Question

Mathematics

Matthew Barr

25 April, 03:29

The distribution of a sample of the outside diameters of PVC pipes approximates a symmetrical, bell-shaped distribution. The arithmetic mean is 14.0 inches, and the standard deviation is 0.1 inches. About 68% of the outside diameters lie between what two amounts? a. 13.5 and 14.5 inchesb. 13.0 and 15.0 inchesc. 13.9 and 14.1 inchesd. 13.8 and 14.2 inches

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Erika · Answer 1

c. 13.9 and 14.1

Step-by-step explanation:

We know that the distribution of the sample of outside diameters of PVC pipes is normal so, the empirical rule can be applied to this data. We have to find 68% percent of the data falls in what data values. These data values can be found through empirical rule as empirical rule states that 68% or 0.68 of the data occurs inside one standard deviation.

The mean μ is 14 inches and standard deviation σ is 0.1 inches.

μ-σ=14-0.1=13.9 and μ+σ=14+0.1=14.1.

Thus, 68% of outside diameter falls between 13.9 and 14.1 inches.