(a)
What proportion of rings will have inside diameters exceeding 10.075 centimeters?
(b)
What is the probability that a piston ring will have an inside diameter between 9.97
and 10.03 centimeters?
(c)
Below what value of inside diameter will 15% of the piston rings fall?
Q4: The yield of a chemical process is being studied. From previous experience yield is
known to be normally distributed and
σ =
3. The past five days of plant operation have
resulted in the following percent yields: 91.6, 88.75, 90.8, 89.95, and 91.3. Find a 95%
confidence interval on the true
mean yield.
Q5: The life in hours of a 75-watt light bulb is known to be normally distributed with
σ =
25 hours. A random sample of 20 bulbs has a mean life
𝑥̅ = 1014
of hours. Construct a
95% confidence interval on the
mean life. Suppose that in we wanted to be 95%
confident

MATH 411
Probability& Statistics
Homework 5
Dr. Hany Nasr Hassan
that the error in estimating the mean life is less than 5 hours. What sample size should be
used?
Q6: The brightness of a television picture tube can be evaluated by measuring the amount
of current required to achieve a particular brightness level. A sample of 10 tubes results
in
𝑥̅ = 317.2
and
𝑠 = 15.7
.
Find (in microamps) a 99% confi
dence interval on mean
current required.
Q7: A particular brand of diet margarine was analyzed to determine the level of
polyunsaturated fatty acid (in percentages). A sample of six packages resulted in the
following data: 16.8, 17.2, 17.4, 16.9, 16.5, 17.1.
Find a 99% confidence interval on t
he
mean
μ
.

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