What is the percent of change from 92 to 108? Round to the nearest percent. [?]%
2 answers:
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Answer:
Probability that the diameter of a selected bearing is greater than 111 millimeters is 0.1056.
Step-by-step explanation:
We are given that the diameters of ball bearings are distributed normally. The mean diameter is 106 millimeters and the standard deviation is 4 millimeters.
<em>Firstly, Let X = diameters of ball bearings</em>
The z score probability distribution for is given by;
Z = ~ N(0,1)
where, = mean diameter = 106 millimeters
= standard deviation = 4 millimeter
Probability that the diameter of a selected bearing is greater than 111 millimeters is given by = P(X > 111 millimeters)
P(X > 111) = P( >
) = P(Z > 1.25) = 1 - P(Z
1.25)
= 1 - 0.89435 = 0.1056
Therefore, probability that the diameter of a selected bearing is greater than 111 millimeters is 0.1056.
Given the CDF
we have PDF
Note that
is wait-time given in hours, so we need to convert from minutes to hours:
so we're looking for
.
The CDF gives us this value right away, since
for any continuous random variable with distribution function 
:
To use the PDF, we need to integrate:
we have PDF
Note that
so we're looking for
The CDF gives us this value right away, since
To use the PDF, we need to integrate: