In: Advanced Math

From a shipment of 75 transistors, 5 of which are defective, a sample of 6 transistors is selected at random.

(a) In how many different ways can the sample be selected?

(b) How many samples contain exactly 3 defective transistors?

(c) How many samples do not contain any defective transistors?

A shipment contains 200 items of which 50 are defective. A sample of 16 items from the shipment is selected at random without replacement. We accept the shipment if at most 3 items in the sample are defective. (a) Write down (but do not evaluate) an exact formula for the probability of acceptance. (b) Use a Table to give the decimal value for the binomial approximation of the probability of acceptance. Show your work. (c) Suppose instead that the shipment contains 500 items of...

In a gross (144) of transistors, there are 2 defective ones.
Three (3) transistors are selected randomly. a. what is the number
of ways one can select exactly one defective transistor among the
three? b. what is the probability of selecting exactly one
defective transistor among the three?

In a shipment of 15 components of a particular computer model, 5
components are defective.
For exercises 1 & 2, let X be the number of defective
components discovered when 4 of them are randomly selected for
inspection.
1. Define the probability mass function of X.
2. What is the probability that at least 2 defective components
are discovered during the inspection?

A shipment of 6 television sets contains 2 defective sets. A
hotel makes a random purchase of 3 of the sets. If x is the number
of defective sets purchased by the hotel, find the cumulative
distribution function of the random variable X representing the
number of defective. Then using F(x), find
(a)P(X= 1) ;
(b)P(0< X≤2).

5. A shipment of 50 light bulbs contains 10 defective light
bulbs. In order to test the quality of the shipment, a quality
control engineer selects 5 light bulbs at random.
(a) How many different samples are possible?
(b) What is the probability the engineer will select exactly two
defective light bulbs?
(c) The shipment will be rejected if at least one of the light
bulbs in the sample is defective. What is the probability the
sample will be rejected?...

Suppose a shipment of 140 electronic components contains 4
defective components. To determine whether the shipment should be
accepted, a quality control engineer randomly selects 4 of the
components and test them. If 1 or more of the components is
defective, the shipment is rejected. what is the probability that
the shipment rejected?

7) A shipment of 10 items contains 4 items which are defective.
If we randomly select 4 of the items for inspection, what is the
probability of at least 3 non-defective items in the sample? Assume
sampling without replacement.
a) 185/210 b) 184/210 c) 25/210 d) 115/210* e) 175/210

1) A paper reports the number of defective transistors across a
square centimeter of an integrated circuit follows the Poisson
distribution with λ = 100. But you're interested in the
distribution of defective transistors over half that area. What
value should λ be?
Answer is 50 but I don't understand why.
2) Wine is considered properly handled if the stored temperature
is within 1 standard deviation of the mean. If wine is shipped in
batches of 20 bottles, in the...

Suppose that the proportion θ of defective items in a large
shipment is unknown, and that the prior distribution of θ is a beta
distribution for which the parameters are α = 2 and β = 200. If 100
items are selected at random from the shipment and if three of
these items are found to be defective, what is the posterior
distribution of θ?

From a lot containing 25 items, 5 of which are defective, 4 are
chosen at random. Let X be the number of defective items found.
Obtain the probability distribution of X if (a) the items are
chosen with replacement, (b) the items are chosen without
replacement.

ADVERTISEMENT

ADVERTISEMENT

Latest Questions

- 11.A computer manufacturer estimates that its cheapest screens will last less than 2.8 years. A random...
- 3.For variables measured at the nominal level, what values can the measures of association take on?...
- Briefly discuss how does the incorporation of aggregates influence strength of cement basis materials (hint explain...
- Accounting Theory Question Case 8- 10 Accounting for Prepaids and Deferrals Short term deferrals (prepaid and...
- Pearl Products Limited of Shenzhen, China, manufactures and distributes toys throughout South East Asia. Three cubic...
- IRAC: Ariel, Sebastian, Flounder and Eric each own 20% of the outstanding shares of the common...
- Prepare three cultural competence recommendations for a clinic that provides services in rural areas and to...

ADVERTISEMENT