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

Delaney Hartman

Mathematics

9 May, 06:02

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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Answers (1)

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Grant Campos · 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.