Math 3339
Homework 5 (6.4-6.6; Chapter 7)
Name:__________________________________ PeopleSoft ID:_______________
Instructions:
• Homework will NOT be accepted through email or in person. Homework must be submitted through
CANVAS BEFORE the deadline.
• Total possible points: 100
• You can use RStudio for any of these problems unless otherwise indicated.
1. The inside diameter of a randomly selected piston ring is a random variable following normal
distribution with mean value 12 cm and standard deviation 0.04 cm.
(a) If 𝑋̅ is the sample mean diameter for a random sample of n = 16 rings, where is the sampling
distribution of 𝑋̅ centered, and what is the standard deviation of the 𝑋̅ distribution?
(b) Answer the questions posted in part (a) for a sample size of n =64 rings.
(c) For which of the two random samples, the one of part (a) or the one of part (b), is 𝑋̅ more likely to
be within 0.01 cm of 12 cm? Explain your reasoning.
a
Mathematical Statistics, Wackerly, D. et al (2011)
, a
2. The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square
inch) and has standard deviation 2.
(a) What is the probability that the average fracture strength of 100 randomly selected pieces of this
glass exceeds 14.5?
(b) Find an interval that includes, with probability 0.95, the average fracture strength of 100 randomly
selected pieces of this glass.
3. The breaking strengths of a random sample of 20 bundles of wool fibers have a sample mean 436.5
and a sample standard deviation 11.9.
(a) Construct 90%, 95%, and 99% confidence intervals for the average breaking strength of the wool
fibers.
(b) Compare the widths of the three confidence intervals. At which level of confidence do you have
the widest interval?
(c) Do you think it is plausible that the average breaking strength is equal to 450?
a
Mathematical Statistics, Wackerly, D. et al (2011)
Homework 5 (6.4-6.6; Chapter 7)
Name:__________________________________ PeopleSoft ID:_______________
Instructions:
• Homework will NOT be accepted through email or in person. Homework must be submitted through
CANVAS BEFORE the deadline.
• Total possible points: 100
• You can use RStudio for any of these problems unless otherwise indicated.
1. The inside diameter of a randomly selected piston ring is a random variable following normal
distribution with mean value 12 cm and standard deviation 0.04 cm.
(a) If 𝑋̅ is the sample mean diameter for a random sample of n = 16 rings, where is the sampling
distribution of 𝑋̅ centered, and what is the standard deviation of the 𝑋̅ distribution?
(b) Answer the questions posted in part (a) for a sample size of n =64 rings.
(c) For which of the two random samples, the one of part (a) or the one of part (b), is 𝑋̅ more likely to
be within 0.01 cm of 12 cm? Explain your reasoning.
a
Mathematical Statistics, Wackerly, D. et al (2011)
, a
2. The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square
inch) and has standard deviation 2.
(a) What is the probability that the average fracture strength of 100 randomly selected pieces of this
glass exceeds 14.5?
(b) Find an interval that includes, with probability 0.95, the average fracture strength of 100 randomly
selected pieces of this glass.
3. The breaking strengths of a random sample of 20 bundles of wool fibers have a sample mean 436.5
and a sample standard deviation 11.9.
(a) Construct 90%, 95%, and 99% confidence intervals for the average breaking strength of the wool
fibers.
(b) Compare the widths of the three confidence intervals. At which level of confidence do you have
the widest interval?
(c) Do you think it is plausible that the average breaking strength is equal to 450?
a
Mathematical Statistics, Wackerly, D. et al (2011)
