Question
In: Statistics and Probability
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75...
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower and upper specification limits under which the ball bearing can operate are 0.735 inch (lower) and 0.765 inch (upper). Past experience has indicated that the actual diameter of the ball bearings is approximately normally distributed, with a mean of 0.755 inch and a standard deviation of 0.006 inch. Suppose a random sample of 2121 ball bearings are selected. Complete parts (a) through (e).
a. What is the probability that the sample mean is between the target and the population mean of 0.755?
(Type an integer or decimal rounded to four decimal places as needed.)
b. What is the probability that the sample mean is between the lower specification limit and the target?
(Type an integer or decimal rounded to four decimal places as needed.)
c. What is the probability that the sample mean is greater than the upper specification limit?
(Type an integer or decimal rounded to four decimal places as needed.)
d. What is the probability that the sample mean is less than the lower specification limit?
(Type an integer or decimal rounded to four decimal places as needed.)
e. The probability is 93% that the sample mean diameter will be greater than what value?
Solutions
orchestra answered 2 years agoRelated Solutions
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.74...
An industrial sewing machine uses ball bearings that are
targeted to have a diameter of 0.74 inch. The lower and upper
specification limits under which the ball bearings can operate are
0.72 inch and 0.76 inch, respectively. Past experience has
indicated that the actual diameter of the ball bearings is
approximately normally distributed, with a mean of 0.743 inch and
a standard deviation of 0.005 inch.
A. What is the probability that a ball bearing is between the
target and...
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.73...
An industrial sewing machine uses ball bearings that are
targeted to have a diameter of 0.73 inch. The lower and upper
specification limits under which the ball bearing can operate are
0.715 inch (lower) and 0.745 inch (upper). Past experience has
indicated that the actual diameter of the ball bearings is
approximately normally distributed, with a mean of 0.734 inch and
a standard deviation of 0.006 inch. Suppose a random sample of 22
ball bearings are selected. Complete parts (a)...
2. An industrial sewing machine uses ball bearings that are targeted to have a diameter of...
2. An industrial sewing machine uses ball bearings that are
targeted to have a diameter of 0.75 inches. The lower and upper
specification limits under which the ball bearings can operate
properly are 0.74 inches and 0.76 inches, respectively.
Past experience has indicated that the actual diameter of the
ball bearings is approximately normally distributed with a mean of
0.753 inches and a standard deviation of 0.004 inches.
What is the probability that a ball bearing is:
a. between the...
A particular type of ballpoint pen uses minute ball bearings that are targeted to have a...
A particular type of ballpoint pen uses minute ball bearings
that are targeted to
have a diameter of 0.5 mm. The lower and upper speci cation limits
under which the
ball bearing can operate are 0.49 mm (lower) and 0.51 mm (upper).
Past experience
has indicated that the ball bearings are approximately normally
distributed with a
mean of 0.503 mm and a standard deviation of 0.004 mm. If you
select a sample of 25
ball bearings, what is the probability...
In an industrial process, 20 mm diameter spherical steel ball bearings are heat-treated to improve their...
In an industrial process, 20 mm diameter spherical steel ball
bearings are heat-treated to improve their durability. For
application (1), the entire ball bearing needs to be heated evenly
to 1000 K. For application (2), only the outer 1 mm of the ball is
to be heated to a temperature in excess of 1000 K. The properties
of the ball bearing are c = 0.5 kJ/kg*K; p = 7800
kg/m3; k = 50 W/m.K. At your facility, you have access...
A simple random sample of 25 ball bearings is selected. The mean diameter of the ball...
A simple random sample of 25 ball bearings is selected. The mean
diameter of the ball bearings is 3mm with a standard deviation of
0.05mm. Previous investigations suggest that the diameters measures
are normally distributed. Construct a 95% confidence interval for
the standard deviation of the diameters of the ball bearings in
this population. Explain how you found your answer.
Manufacturing Ball bearings are manufactured with a mean diameter of 6 millimeter (mm).
Manufacturing Ball bearings are manufactured with a mean diameter of 6 millimeter (mm). Because of variability in the manufacturing process, the diameters of the ball bearings are approximately normally distributed with a standard deviation of 0.03 mm.
a) What proportion of ball bearings has a diameter more than 6.04 mm ?
b) Any ball bearings that have a diameter less than 5.95 mm or greater than 6.05 mm are discarded. What proportion of ball bearings will be discarded ?
c) ...
The diameters of ball bearings are distributed normally. The mean diameter is 89 millimeters and the...
The diameters of ball bearings are distributed normally. The
mean diameter is 89 millimeters and the standard deviation is 5
millimeters. Find the probability that the diameter of a selected
bearing is between 91 and 97 millimeters. Round your answer to four
decimal places.
The true average diameter of ball bearings of a certain type is supposed to be 0.5...
The true average diameter of ball bearings of a certain type is
supposed to be 0.5 in. A one-sample t test will be carried
out to see whether this is the case. What conclusion is appropriate
in each of the following situations?
(a)
n = 10, t = 1.51, α = 0.05
Reject the null hypothesis. There is sufficient evidence that
the true diameter differs from 0.5 in.
Reject the null hypothesis. There is not sufficient evidence
that the true...
The true average diameter of ball bearings of a certain type is supposed to be 0.5...
The true average diameter of ball bearings of a certain type is
supposed to be 0.5 inch.
What conclusion is appropriate when testing H0: μ =
0.5 versus Ha: μ ≠ 0.5 inch in each of the following
situations?
(a)
n = 15, t = 1.8, α = 0.05
1. Reject H0
2.Fail to reject
H0
(b)
n = 15, t = −1.8, α = 0.05
1. Reject H0
2. Fail to reject
H0
(c)
n = 27, t =...
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