If merchandise inventory is being valued at cost and the price level is decreasing, which of the three methods of costing - FIFO, LIFO, or Weighted Average cost - will yield

a. the highest inventory cost

b. the lowest inventory cost

c. the highest gross profit

d. the lowest gross profit

please explain the answer thoroughly.

A vertical summit curve has tangent grades of +2.5% and -1.5% intersecting at station 12+460.12 at an elevation of 150m above sea level. If the length of the curve is 182m: a. Compute the length of the passing sight distance.

b. Compute the stationing of the highest point of the curve.

c. Compute the elevation of the highest point of the curve.

The number of imperfections in an object has a Poisson distribution with a mean λ = 8.5. If the number of imperfections is 4 or less, the object is called "top quality." If the number of imperfections is between 5 and 8 inclusive, the object is called "good quality." If the number of imperfections is between 9 and 12 inclusive, the object is called "normal quality." If the number of imperfections is 13 or more, the object is called "bad quality." The numbers of imperfections in different objects are independent of each other. A random sample set of seven objects is taken. What is the probability that the sample set has exactly two top quality, two good quality, two normal quality, and one bad quality objects?

During the World War II, rockets were fired to attack the city of London. To manage the crisis, London was subdivided into many identical regions. Ambulances and fire fighters were assigned in each region to observe the number of rocket hits while providing rescue. At the same time, statisticians predicted the number of rocket hits follows Poisson distribution. Using goodness of fit test, test whether or not the number of rocket hits follows a Poisson distribution at α=5%.

It should be tested whether a cube is fair or not. This tells how many times the number 1 appears.

With a sample, a dice is thrown 720 times and it showed number one 95 times. The null hypothesis is Ho:p =1/6. Probability of error is specified α=0.05

a)Approximate the binomial distribution according to Moivre-Laplace by normal distribution (without correction ).

b) derive a formula for the rejected area or accepted area.

A cooler has 6 Gatorades, 2 colas, and 4 waters. You select 3 beverages from the cooler at random. Let B denote the number of Gatorade selected and let C denote the number of colas selected. For example, if you grabbed a cola and two waters, then C = 1 and B = 0.

a) construct a joint probability distribution for B and C.

b) compute E[3B-C^2].

The number of hours a battery lasts before failing follows an exponential distribution with a mean of μ = 24.5 hours and a standard deviation of 10 hours. Eric buys a pack of 64 batteries. Find the probability that the average number of hours a battery lasts is 21 hours or less.

a. 0.0026

b. 0.9974

c. 0.3632

d. -2.80

Solve the problem and show all your work below. Draw appropriate pictures!

(B) A new drug claims to be effective against flu 70% of the time. The drug is tested on 28 selected patients. a) Use Binomial distribution to find the probability that exactly 21 patients recovered from the flu? (Round your answer to the nearest thousandth). b) What is the mean of the number of patients who recovered from the flu? c) What is the variance of the number of patients who recovered from the flu?

We suppose that the number of errors Z within the first year for a fabrication is Poisson distributed with waiting value 2.5. We also know that the number of errors Z wont be overrided or a replacement is needed for the fabrication.

a. Find the probabilility that within that year the errors will occur within the probability ?? = ?? (1 ≤ ?? <5).

b. The manufacturer wants to replace a maximum. 10% of all of the products. What is the minimum errors Z when this occurs?

Many basketball players and fans believe strongly in the “hot hand.” That is, they believe that players tend to shoot in streaks, either makes or misses. If this is the case, why does the binomial distribution not apply, at least not exactly, to the number of makes in a given number of shots? Which assumption of the binomial model is violated, the independence of successive shots, or the constant probability of success on each shot? Or can you tell? Explain your reasoning.