A very large batch of components has arrived at adistributor. The batch can be characterized as acceptableonly if the proportion of defective components isat most .10. The distributor decides to randomlyselect 10 components and to accept the batch only ifthe number of defective components in the sample isat most 2.a. What is the probability that the batch will beaccepted when the actual proportion of defectives is.01? .05? .10? .20? .25?b. Let p denote the actual proportion of defectives inthe batch. A graph of P(batch is accepted) as a function of p, with p on the horizontal axis and P(batch is accepted) on the vertical axis, is called the operatingcharacteristic curve for the acceptance samplingplan. Use the results of part (a) to sketch this curvefor 0 # p # 1.c. Repeat parts (a) and (b) with “1” replacing “2” in theacceptance sampling plan.d. Repeat parts (a) and (b) with “15” replacing “10” inthe acceptance sampling plan.e. Which of the three sampling plans, that of part (a),(c), or (d), appears most satisfactory, and why?
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
A very large batch of components has arrived at a
distributor. The batch can be characterized as acceptable
only if the proportion of defective components is
at most .10. The distributor decides to randomly
select 10 components and to accept the batch only if
the number of defective components in the sample is
at most 2.
a. What is the probability that the batch will be
accepted when the actual proportion of defectives is
.01? .05? .10? .20? .25?
b. Let p denote the actual proportion of defectives in
the batch. A graph of P(batch is accepted) as a
characteristic curve for the acceptance sampling
plan. Use the results of part (a) to sketch this curve
for 0 # p # 1.
c. Repeat parts (a) and (b) with “1” replacing “2” in the
acceptance sampling plan.
d. Repeat parts (a) and (b) with “15” replacing “10” in
the acceptance sampling plan.
e. Which of the three sampling plans, that of part (a),
(c), or (d), appears most satisfactory, and why?
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 25 images
