46. A shipment of pins contains 25 great ones and 2 flawed ones. At the

getting office, an examiner picks three pins aimlessly and tests them. In the event that

any damaged pin is found among the three that are tried, the shipment would be

dismissed.

a. What is the likelihood that the shipment would be acknowledged?

b. To expand the likelihood of acknowledgment to at any rate 90%, it is chosen to

do one of the accompanying:

I. Add some great pins to the shipment.

ii. Eliminate some faulty pins in the shipment.

For every one of the two choices, discover precisely the number of pins ought to be added or

taken out.

A MBA graduate is going after nine positions, and accepts that she has in each

of the nine cases a steady and autonomous 0.48 likelihood of getting an offer.

a. What is the likelihood that she will have at any rate three offers?

b. On the off chance that she needs to be 95% certain of having in any event three offers, the number of

more positions would it be advisable for her to apply for? (Accept every one of these extra applications will likewise have a similar likelihood of accomplishment.)

c. On the off chance that there are close to the first nine positions that she can apply for,

what worth of likelihood of accomplishment would give her 95% certainty of at

least three offers?

The quantity of salvage calls got by a salvage crew in a city follows a Poisson dispersion with 2.83 each day. The crew can deal with all things considered four calls every day.

a. What is the likelihood that the crew will actually want to deal with every one of the calls

on a specific day?

b. The crew needs to have at any rate 95% certainty of having the option to deal with

every one of the calls got in a day. In any event the number of calls a day should the

crew be ready for?

c. Expecting that the crew can deal with all things considered four calls every day, what is the

biggest worth of that would yield 95% certainty that the crew can

handle all calls?

Equal the initial investment Analysis Example

Envision that you need to dispatch another business selling a cell phone application. You make the accompanying suspicions about your expenses and income.

The normal selling cost = $7.

Assessed fixed expenses = $75,000 (this is sufficient to cover your compensation and pay for a little office). These costs won't change with the quantity of applications sold.

Variable expenses = $0.50 (these are the exchange charges you need to pay on every deal).

(1) Armed with this data, ascertain the make back the initial investment point in units:

m25m

(2) To procure a benefit of 5%, what number of units do you have to sell?

(3) What in the event that you had the option to decrease the assessed fixed expense to $65,000, what might your new equal the initial investment be in units?

(4) What on the off chance that you came up short on factor costs and the real factor costs are $1.15, what might your equal the initial investment be in units

only 3(9). 4ta} and 4m] 3_[Random Experiments and Sample Spaces} For each ofthe following random experiments carefullyr describe the sample space, S. anto compute ISL the size of S. and explain your answer. {b} A die is thrown 3 times. {g} ['1 A 4 node. rooted binary.f tree is written down. {Events} Carefully describe the events A. E, A u B. and A n B in the following sample spaces from 3. above. and determine the sizes [number of outcomes] of these evenls. {a} f'} In 3b, A = {at least one even-sscore face}, B = {all faces 4 or more}. {b} H In 3g. A = {the root has two ddren}. E = {the here has height .3}, the height being the number of edges on a longest path from the root to a leaf. \fName: ID: 6. Regarding the random experiment and sample space, which of the following statements is correct? a. In a random experiment, we have no idea what outcome would be. b. If we repeat a random experiment a times, the collection of these n outcomes would form a sample space. c. Even before a random experiment is performed, we know that the outcome must be one of those in the sample space. d. In a random experiment, all outcomes in the sample space are equal likely to happen. 7. Regarding mutual exclusive and independent events, which of the following statements is correct? a. If two events are mutual exclusive, then they are also independent. b. If two events are independent, then they are also mutual exclusive. c. Mutually exclusive events cannot occur at the same time. d. Independent events cannot occur at the same time. 8. When estimate population mean using sample mean, we should a. Use the Central Limit Theorem if the population is normally distributed; b. Use t-distribution if sample size is small and population is normally distributed with unknown variance; c. Use t-distribution if sample size is small and population is normally distributed with known variance; d. Use normal distribution if the population is binomial.\f