Question

In: Statistics and Probability

A weapons manufacturer uses a liquid propellant that can get mixed with another liquid to produce...

A weapons manufacturer uses a liquid propellant that can get mixed with another liquid to produce a contaminated cartridge. A statistician found that 24​% of the cartridges in the particular lot were contaminated. Suppose you randomly sample​ (without replacement) gun cartridges from this lot until you find a contaminated one. Let x be the number of cartridges sampled until a contaminated one is found. It is known that the probability distribution for x is given by the formula shown below. Complete parts a through c. p left parenthesis x right parenthesis equals left parenthesis 0.24 right parenthesis left parenthesis 0.76 right parenthesis Superscript x minus 1​, xequals​1, 2​ ,3 ,... a. Find ​p(1​). Interpret this result. ​p(1​)equals nothing ​(Round to three decimal places as​ needed.) What is the correct interpretation for ​p(1​)? A. This value is the probability that one would encounter a contaminated cartridge on the first trial. B. This value is the probability that one would encounter a contaminated cartridge in one hundred trials. C. This value is the probability that one would encounter a​ non-contaminated cartridge on the first trial. b. Find ​p(5​). Interpret this result. ​p(5​)equals nothing ​(Round to three decimal places as​ needed.) What is the correct interpretation for ​p(5​)? A. This value is the probability that one would first encounter 5 contaminated cartridge in one hundred trials. B. This value is the probability that one would first encounter a contaminated cartridge on the fifth trial. C. This value is the probability that one would first encounter a​ non-contaminated cartridge on the fifth trial. c. Find ​P(xgreater than or equals​2). Interpret this result. Upper P left parenthesis x greater than or equals 2 right parenthesisequals nothing ​(Round to three decimal places as​ needed.) What is the correct interpretation for ​P(xgreater than or equals​2)?

Solutions

Expert Solution

Let x be the number of cartridges sampled until a contaminated one is found.

It is known that the probability distribution for x is given by the formula shown below.

a. Find ​p(1​).

We get ​p(1​)= 0.240

According to the event X, defined in the problem,

A. This value is the probability that one would encounter a contaminated cartridge on the first trial.

b.

We get ​p(5​)= 0.080

B. This value is the probability that one would first encounter a contaminated cartridge on the fifth trial.

c. Find

= 1 - 0.24

= 0.76

= 0.760

Interpretation:

C. This value is the probability that one would first encounter a contaminated cartridge on 2nd or later trial, which is equal to the complementary of the probability that one would encounter a contaminated cartridge on the 1st trial itself.

orchestra answered 1 year ago
Next > < Previous

Related Solutions

Three liquid mixtures, with compositions listed in the table are mixed to produce a single mixture....
Three liquid mixtures, with compositions listed in the table are mixed to produce a single mixture. If the volumetric flowrate of stream 1 (SG 0.868) is 0.12 ft^3/s and the mass flowrate of stream 2 and 3 are 3 kg/s and 3 kg/s draw a fully labeled diagram for the process and find the composition of the product stream. (assume that the process operates at steady state. Liquid Mass composition % Stream 1 Stream 2 Stream 3 C6H6 22 50...
A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along...
A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line.  The machine that dispenses dressings is working properly when the mean amount dispensed is 8 ounces.  The population standard deviation of the amount dispensed is 0.15 ounce.  A sample of 50 bottles is selected periodically, and the filling line is stopped if there is evidence that the mean amount dispensed is different from 8 ounces.  Suppose that the mean amount dispensed in a particular sample...
A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along...
A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressings is working properly when the mean amount dispensed is 8 ounces. The population standard deviation of the amount dispensed is 0.15 ounce. A sample of 50 bottles is selected periodically, and the filling line is stopped if there is evidence that the mean amount dispensed is different from 8 ounces. Suppose that the mean amount dispensed...
A drug manufacturer uses two production facilities to produce a pain reliever. The amount of the...
A drug manufacturer uses two production facilities to produce a pain reliever. The amount of the active ingredient of the drug in the capsules at the two​ facilities, X1 and X2, are normally distributed random variables. The desire of the quality control manager is that the population mean amounts of the active ingredient in the​ capsules, μ1 and μ2​, be equal. Recent tests on small samples have indicated a noticeable increase in the amount of the active ingredient in capsules...
If Blue country uses it resources to produce q-tips, it can produce 100 units. For the...
If Blue country uses it resources to produce q-tips, it can produce 100 units. For the same resources, Blue country could choose to produce 25 units of pens. For Green country, it is either 90 units of q-tips or 30 units of pens. Alright, first of all, who has the absolute advantage in q-tips, pens? Who has the comparative advantage in q-tips, pens? Should this countries trade? If so, at what “price” range?
how can CFO and CHRO benefit one another in an organization? what benefits can one get...
how can CFO and CHRO benefit one another in an organization? what benefits can one get from one another and how can one better one another?
A manufacturer uses a new production method to produce steel rods. A random sample of 17...
A manufacturer uses a new production method to produce steel rods. A random sample of 17 steel rods resulted in lengths with a standard deviation of 2.1 cm. At the 0.05 significance level, test the claim that the new production method has lengths with a standard deviation different from 3.5 cm, which was the standard deviation for the old method. Use the p-value method. Initial Claim: Null Hypothesis: Alternative Hypothesis Test statistic (make sure you state which test statistic that...
A manufacturer uses a new production method to produce steel rods. A random sample of 17...
A manufacturer uses a new production method to produce steel rods. A random sample of 17 steel rods resulted in lengths with a standard deviation of 4.7 cm. At the 0.10 significance level, test the claim that the new production method has lengths with a standard deviation different from 3.5 cm, which was the standard deviation for the old method.
A chemical manufacturer uses chemicals 1 and 2 to produce two drugs. Drug 1 must be...
A chemical manufacturer uses chemicals 1 and 2 to produce two drugs. Drug 1 must be at least 70% chemical 1, and drug 2 must be at least 60%
chemical 2. Up to 50,000 ounces of drug 1 can be sold at $30 per ounce; up to 60,000 ounces of drug 2 can be sold at $25 per ounce. Up to 45,000 ounces of chemi- cal 1 can be purchased at $15 per ounce, and up to 55,000 ounces of...
A chemical manufacturer uses chemicals 1 and 2 to produce two drugs. Drug 1 must be...
A chemical manufacturer uses chemicals 1 and 2 to produce two drugs. Drug 1 must be at least 25% chemical 1, and drug 2 must be at least 60% chemical 2. Up to 50,000 ounces of drug 1 can be sold at $27 per ounce; up to 60,000 ounces of drug 2 can be sold at $26 per ounce. Up to 45,000 ounces of chemical 1 can be purchased at $19 per ounce, and up to 55,000 ounces of chemical...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT