A manufacturer produces gears for use in an engine’s transmission that have a mean diameter of 10.00 mm and a standard deviation of 0.03 mm. The length of these diameters follows the normal distribution. What is the probability that a randomly selected gear has a diameter between 9.96 mm and 10.01 mm?
2 answers:
Answer: 0.2789
Step-by-step explanation:
Given: Mean :
Standard deviation :
The formula to calculate z-score is given by :_
For x= 9.96 mm, we have
For x= 10.01 mm, we have
The P-value =
Hence, the probability that a randomly selected gear has a diameter between 9.96 mm and 10.01 mm = 0.2789
Answer:
Pr=0.2894
Step-by-step explanation:
given mean diameter =10 mm
standard deviation=0.03 mm
z equation is
z=x-μ/σ
The problem has two values of x
for x=9.96
z=-1.33
for x-10.01
z=0.33
from Probability table we have
Pr(-1.33<z<0.33)=pr(z<0.33)-pr(z>-1.33)
Pr=0.2894
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