Part 1 a. What is the probability that a ball bearing is between the target and the actual mean? enter your response here (Round to four decimal places as needed.) b. What is the probability that a ball bearing is between the lower specification limit and the target? enter your response here (Round to four decimal places as needed.) c. What is the probability that a ball bearing is above the upper specification limit?
Part 1 a. What is the probability that a ball bearing is between the target and the actual mean? enter your response here (Round to four decimal places as needed.) b. What is the probability that a ball bearing is between the lower specification limit and the target? enter your response here (Round to four decimal places as needed.) c. What is the probability that a ball bearing is above the upper specification limit?
Part 1 a. What is the probability that a ball bearing is between the target and the actual mean? enter your response here (Round to four decimal places as needed.) b. What is the probability that a ball bearing is between the lower specification limit and the target? enter your response here (Round to four decimal places as needed.) c. What is the probability that a ball bearing is above the upper specification limit?
An industrial sewing machine uses ball bearings that are targeted to have a diameter of
0.78
inch. The lower and upper specification limits under which the ball bearings can operate are
0.77
inch and
0.79
inch, respectively. Past experience has indicated that the actual diameter of the ball bearings is approximately normally distributed, with a mean of
0.783
inch and a standard deviation of
0.003
inch. Complete parts (a) through (e) below.
Question content area bottom
Part 1
a. What is the probability that a ball bearing is between the target and the actual mean?
enter your response here
(Round to four decimal places as needed.)
b. What is the probability that a ball bearing is between the lower specification limit and the target?
enter your response here
(Round to four decimal places as needed.)
c. What is the probability that a ball bearing is above the upper specification limit?
enter your response here
(Round to four decimal places as needed.)
d. What is the probability that a ball bearing is below the lower specification limit?
enter your response here
(Round to four decimal places as needed.)
e. Of all the ball bearings,
91%
of the diameters are greater than what value?
enter your response here
inch (Round to three decimal places as needed.)
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.
