SOLUTION: 4. Suppose that 7% of the bolts produced by a machine are defective. If 10 bolts are chosen from a huge shipment and inspected, determine the probability that a. exactly one

Algebra ->  Probability-and-statistics -> SOLUTION: 4. Suppose that 7% of the bolts produced by a machine are defective. If 10 bolts are chosen from a huge shipment and inspected, determine the probability that a. exactly one      Log On


   

Question 346629: 4. Suppose that 7% of the bolts produced by a machine are defective. If 10 bolts are chosen from a huge shipment and inspected, determine the probability that
a. exactly one bolt is defective
b. at least two bolts are defective
c. at most one bolt is defective
d. at least one bolt is defective.
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For 0 failures,P=1%2A%280.93%29%5E10%2A%280.07%29%5E0=0.48398
For 1 failure, P=10%2A%280.93%29%5E9%2A%280.07%29%5E1=0.36429
For 2 failures,P=45%2A%280.93%29%5E8%2A%280.07%29%5E2=0.12339
Those are the only values we need to solve the problem.
.
.
Now let's work through the problem.
a) Exactly 1 bolt failure, highlight%28P=0.36429%29
.
.
b) At least 2 bolt failures, means 2 failures or more.
In other words, not 0 or 1 failures(1-%28P%280%29%2BP%281%29%29).
P%280%29%2BP%281%29=0.48398%2B0.36429=0.84825
You know that

So then,



.
.
c)At most 1 bolt, means 0 or 1 failures.
P%280%29%2BP%281%29=highlight%280.84825%29
.
.
d)At least 1 bolt failure, means not 0 failures (1-P%280%29).

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose that 7% of the bolts produced by a machine are defective. If 10 bolts are chosen from a huge shipment and inspected, determine the probability that
----
Binomial Problem with n=10 and p = 0.07
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a. exactly one bolt is defective
P(x=1) = 10C1(0.07)*(0.93)^9 = binompdf(10,0.07,1) = 0.3643
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b. at least two bolts are defective
Ans: 1-binomcdf(10,0.07,1) = 0.1517
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c. at most one bolt is defective
Ans: binomcdf(10,0.07,1) = 0.8483
-----------------------------------------
d. at least one bolt is defective.
Ans: 1-binomcdf(10,0.07,0) = 0.5160
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Cheers,
Stan H.