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In metal fabrication unit, steel rods of a particular type have lengths with standard deviation 0.01 in. (a) Assume that the lengths are normally distributed with mean and specifications on this length are 33.7 in. +0.025 in.. What fraction of the lengths of rods actually satisfy this specification, if µ = 33.7 in.? fraction = (Round your answer to three decimal places.) (b) If lengths are normally distributed with a mean of 33.69 in. (and same standard deviation as above), evaluate the probability that at least 8 of the next 10 steel rods produced are within the specifications of 33.7 in. + 0.025 in.. probability = (Round your answer to three decimal places.) (c) Let š denote the sample mean length of 64 rods of this type. Approximate the probability that is X within 0.001 in. of H. probability = (Round your answer to three decimal places.)

In metal fabrication unit, steel rods of a particular type have lengths with standard deviation 0.01 in. (a) Assume that the lengths are normally distributed with mean and specifications on this length are 33.7 in. +0.025 in.. What fraction of the lengths of rods actually satisfy this specification, if µ = 33.7 in.? fraction = (Round your answer to three decimal places.) (b) If lengths are normally distributed with a mean of 33.69 in. (and same standard deviation as above), evaluate the probability that at least 8 of the next 10 steel rods produced are within the specifications of 33.7 in. + 0.025 in.. probability = (Round your answer to three decimal places.) (c) Let š denote the sample mean length of 64 rods of this type. Approximate the probability that is X within 0.001 in. of H. probability = (Round your answer to three decimal places.)

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter29: Tolerance, Clearance, And Interference
Section: Chapter Questions
Problem 16A: Spacers are manufactured to the mean dimension and tolerance shown in Figure 29-12. An inspector...
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In metal fabrication unit, steel rods of a particular type have lengths with standard deviation 0.01 in. (a) Assume that the lengths are normally distributed with mean u and specifications on this length are 33.7 in. + 0.025 in.. What fraction of the lengths of rods actually satisfy this specification, if u = 33.7 in.? fraction = (Round your answer to three decimal places.) (b) If lengths are normally distributed with a mean of 33.69 in. (and same standard deviation as above), evaluate the probability that at least 8 of the next 10 steel rods produced are within the specifications of 33.7 in. + 0.025 in.. probability = (Round your answer to three decimal places.) (c) Let x denote the sample mean length of 64 rods of this type. Approximate the probability that is X within 0.001 in. of H. probability = (Round your answer to three decimal places.)
Transcribed Image Text:In metal fabrication unit, steel rods of a particular type have lengths with standard deviation 0.01 in. (a) Assume that the lengths are normally distributed with mean u and specifications on this length are 33.7 in. + 0.025 in.. What fraction of the lengths of rods actually satisfy this specification, if u = 33.7 in.? fraction = (Round your answer to three decimal places.) (b) If lengths are normally distributed with a mean of 33.69 in. (and same standard deviation as above), evaluate the probability that at least 8 of the next 10 steel rods produced are within the specifications of 33.7 in. + 0.025 in.. probability = (Round your answer to three decimal places.) (c) Let x denote the sample mean length of 64 rods of this type. Approximate the probability that is X within 0.001 in. of H. probability = (Round your answer to three decimal places.)
Expert Solution
Step 1

a)

The Z-score of a random variable X is defined as follows:

Z = (X – µ)/σ.

Here, µ and σ are the mean and standard deviation of X, respectively.

Step 2

Consider a random variable X that is the length of steel rod.

According to the given information X follows normal distribution with mean μ = 33.7 in and standard deviation of σ = 0.01 in.

The proportion of lengths of rods actually satisfy this specification of 33.7 ± 0.025 is,

Statistics homework question answer, step 2, image 1

Thus, the fraction of lengths of rods actually satisfy this specification of 33.7 ± 0.025 is 0.988.

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