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A plate is attached to its base by 10 bolts. Each bolt is
Chapter 4, Problem 14SE(choose chapter or problem)
A plate is attached to its base by 10 bolts. Each bolt is inspected before installation, and the probability of passing the inspection is 0.9. Only bolts that pass the inspection are installed. Let X denote the number of bolts that are inspected in order to attach one plate.
a. Find P (X = 12).
b. Find \(\mu_{x}\) .
c. Find \(\sigma_{x}\) .
Equation transcription:
Text transcription:
\mu_{x}
\sigma_{x}
Questions & Answers
QUESTION:
A plate is attached to its base by 10 bolts. Each bolt is inspected before installation, and the probability of passing the inspection is 0.9. Only bolts that pass the inspection are installed. Let X denote the number of bolts that are inspected in order to attach one plate.
a. Find P (X = 12).
b. Find \(\mu_{x}\) .
c. Find \(\sigma_{x}\) .
Equation transcription:
Text transcription:
\mu_{x}
\sigma_{x}
ANSWER:
Solution :
Step 1 of 3:
Let X denote the number of bolts that are inspected in order to attach one plate.
Now a plate is attached to its base by 10 bolts.
So X=10.
Then the probability of passing the inspection is 0.9.
So the probability of success is 0.9.
Here X
So .
Our goal is :
a). We need to find P(X=12).
b). We need to find .
c). We need to find .
a).
Now we have to find P(X=12).
The formula of the negative binomial is
B(X,r,P)=
Where X is the trials and
r is the success.
Then the P(X=12) is
B(12,10,0.9)=or
P(X=12)=
P(X=12)=
P(X=12)=
P(X=12)=
P(X=12)=
Therefore P(X=12) is 0.1918.