Question

In: Statistics and Probability

A bulletproof vest manufacturer has 1000 bulletproof vests for sale. Each vest has a 5% probability...

A bulletproof vest manufacturer has 1000 bulletproof vests for sale. Each vest has a 5% probability of experiencing a failure resulting in a serious injury or death. You randomly select 200 vests for potential purchase.

What is the likelihood that 10 vests will experience a failure resulting in a serious injury or death? [Show your work]

What is the likelihood that they will all be free from defect? [Show your work]

What is the likelihood that they will all experience a failure resulting in serious injury or death? [Show your work]

Expert Solution

Sample size = n =200

Probability of failure = p = 0.05

This can be approximated by normal distribution since n is large and

n*p = 200*0.05 =10 and is greater than 5.

The normal approximation is given by:

Mean

Variance :

= 3.08211

What is the likelihood that 10 vests will experience a failure resulting in a serious injury or death?

The probability that 10 vests fail out of 200 is given by:

Applying continuity correction,

=0.5636 - 0.4364

=0.1272

The likelihood that 10 vests will experience a failure resulting in a serious injury or death is 0.1272.

What is the likelihood that they will all be free from defect?

Probability that all vests are free of defect is given by

=0.0010-0.0003

=0.0007

The likelihood that all vests will be free from defect is 0.0007.

What is the likelihood that they will all experience a failure resulting in serious injury or death?

Probability that all vests experience a failure resulting in serious injury or death is given by:

61.484< Z< 61.8085

0.0000

The likelihood that all vests experience a failure resulting in serious injury or death is is 0.0000.

orchestra answered 1 year ago

Consider a hard disk drive that has 5 double-sided platters, each surface has 1000 tracks, each...

Consider a hard disk drive that has 5 double-sided platters, each surface has 1000 tracks, each track has 256 sectors of size 512 bytes. Each block (disk page) comprises of 8 sectors. The seek time between adjacent tracks in 1ms and the average seek time between two random tracks is 25ms. The disk rotates at a speed of 7200 rpm (revolutions per minute). Let’s say, we have a file of size 1 MB and it contains 2048 equal-sized records. 1....

5) A manufacturer of clothing knows that the probability of a button flaw (broken, sewed on...

5) A manufacturer of clothing knows that the probability of a button flaw (broken, sewed on incorrectly, or missing) is 0.002. An inspector examines 56 shirts in an hour, each with 4 buttons. Using a Poisson probability model, answer parts a and b below. a) What is the probability that she finds no button flaws? The probability that the inspector finds no button flaws is___ .(Round to three decimal places as needed.) b) What is the probability that she finds...

Consider two bonds. Each has a face value of $1000 and matures in 5 years. One...

Consider two bonds. Each has a face value of $1000 and matures in 5 years. One has no coupon payment, and the other pays $100 per year. Calculate the present value of each bond if the interest rate is 4 percent and if the interest rate is 8 percent. (Show Work)

An industry has 1000 firms, each with the production function f(x1; x2 ) x1^.5 x2^.5. Theprice...

An industry has 1000 firms, each with the production function f(x1; x2 ) x1^.5 x2^.5. Theprice of factor 1 is 1 and the price of factor 2 is 1. In the long run, both factors are variable, but inthe short run, each firm is stuck with using 100 units of factor 2.The long run industry supply curve:Can somebody explain how to solve?

If $1000 is deposited at the end of each year for 5 years into an ordinary...

If $1000 is deposited at the end of each year for 5 years into an ordinary annuity earning 7.59% compounded annually, construct a balance sheet showing the interest earned during each year and the balance at the end of each year. Complete the balance sheet. Period Amount Interest Balance 1 $1000.00 2 $1000.00 3 $1000.00 4 $1000.00 5 $1000.00 (Round to the nearest cent as needed.)

A surgeon performs 5 surgeries in a week. Each surgery has 0.1 probability of developing complications....

A surgeon performs 5 surgeries in a week. Each surgery has 0.1 probability of developing complications. If the surgeries are independent find: a. The probability all 5 surgeries develop complications b. The probability at least one of the surgeries develop complications. c. Exactly two of the surgeries develop complications

A manufacturer of computer memory chips produces chips in lots of 1000. If nothing has gone...

A manufacturer of computer memory chips produces chips in lots of 1000. If nothing has gone wrong in the manufacturing process, at most 5 chips each lot would be defective, but if something does go wrong, there could be far more defective chips. If something goes wrong with a given lot, they discard the entire lot. It would be prohibitively expensive to test every chip in every lot, so they want to make the decision of whether or not to...

2. The following probability distribution of the monthly incomes (X in $1000) of account executives has...

2. The following probability distribution of the monthly incomes (X in $1000) of account executives has been estimated for a big accounting firm. a. Find the expected value and the standard deviation of the monthly incomes. b. A random sample of 64 executives is taken. What is the probability that the sample mean value exceeds $20,500? X 12 14 20 22 30 P(X) 0.15 0.15 0.4 0.2 0.1

Find the present value of $1000 paid at the end of each month for 5 years...

Find the present value of $1000 paid at the end of each month for 5 years at 12% compounded semi-annually If possible, please use in terms of a financial calculator

A clothing company has 100 yards of cloth and produces shirts (x units) and vests (y...

A clothing company has 100 yards of cloth and produces shirts (x units) and vests (y units). Shirts require 10 units and have profit value of $5, while vests require 4 units and have profit value of $4. What is the optimal production solution? What if the company decides to also put a “non-zero constraint” on all production? Must produce at least 3 shirts and 10 vests.