Most exhibition shows open in the morning and close in the late evening. A study of Saturday arrival times showed that the average arrival time was 3 hours and 48 minutes after the doors opened, and the standard deviation was estimated at about 57 minutes. Assume that the arrival times follow a normal distribution.

(a) At what time after the doors open will 86% of the people who are coming to the Saturday show have arrived? (Round your answer to the nearest number of minutes.)
  minutes after doors open

(b) At what time after the doors open will only 12% of the people who are coming to the Saturday show have arrived? (Round your answer to the nearest number of minutes.)
minutes after doors open

(c) Do you think the probability distribution of arrival times for Friday might be different from the distribution of arrival times for Saturday? Explain your answer.

match vocab with definition

Alexandra Marcus, manager of the Sky Club Hotel, has requested your assistance on a queuing issue to improve the guest service at the hotel. Alexandra Marcus is considering how to restructure the front desk to reach an optimal level of staff efficiency and guest service. Observation of arrivals during the peak check-in time of 3:00PM to 5:00PM shows that an average of 80 guests arrive each hour. It takes an average of 3 minutes for the front-desk clerk to register each guest. At present, the hotel has five clerks on duty, each with a separate waiting line.

PLEASE SHOW CALCULATIONS!!

a. Average utilization rate of a server (p)

b. The probability of no. customers in the system (Po)

c. Average number of customers in the system (L)

d. Average time in the system (W)

e. Average waiting in line (Wq)

f. Average number of customers in line waiting Lq

Your goal is to collect all 80 player cards in a game. The Player cards are numbered 1 through 80. High numbered cards are rarer/more valuable than lower numbered cards.

Albert has a lot of money to spend and loves the game. So every day he buys a pack for $100. Inside each pack, there is a random card. The probability of getting the n-th card is c(1.05)^-n, For some constant c. Albert buys his first pack on June 1st. What is the expected number of Player cards Albert will collect in June?(30 days)

a.) Find an exact, closed-form expression for c. (Answer should not include a summation symbol or integral sign).

b.)Find the expected number of unique Player cards Albert will collect in June. (Answer may include summation symbol or integral sign.

1) The number of times that student takes an A class, X(X has a line under) has the discrete uniform pmf: p(x) = 0.25 for x = 1,2,3,4. Recall from earlier course material that this pmf has E(X)(X has a line under)=5/2 and V(X)(X has a line under)= 15/12. A random sample of 36 students will be selected and the number of times that have taken A class will be recorded.
-Determine the probability that the mean of this sample is less that 3.

2)The lysine composition is soybean meal was measured in 9 random samples resulting in a sample mean of 22.4 g/kg and standard deviation of 1.2g/kg. Construct a 2-sided 99% confidence interval on the population standard deviation. Assume that the population is normally distributed. What is the estimated of the lower bound of this confidence interval?

2. Three fair dice are rolled. Let X be the sum of the 3 dice.

(a) What is the range of values that X can have?

(b) Find the probabilities of the values occuring in part (a); that is, P(X = k) for each k in part (a). (Make a table.)

3. Let X denote the difference between the number of heads and the number of tails obtained when a coin is tossed n times.

(a) What are the possible values of X?

(b) Suppose that the coin is fair, and that n = 3. What are the probabilities associated with each of the values that X can take?

7. An urn holds 10 red and 6 green marbles. A fair coin is tossed. If we get heads, two marbles are selected from the urn. Otherwise three marbles are selected. If we have only reds, what is the probability that we selected exactly two marbles?

Regarding problem R2 from chapter 26. Make a box representing a roulette wheel with 18 tickets that represent red and 20 that represent black or green. Draw 3800 times with replacement from this box and record the number of tickets drawn that are red. Repeat this process 10,000 times. What is the fraction of times (out of these 10,000 repeated trials) were the number of red tickets drawn at least 1,890? How does this compare to the P-value you got in the problem? Can you use pbinom( ) to compute this probability? Are these numbers different? Why?

"With a perfectly balanced roulette wheel, in the long run, red numbers should turn up 18 times in 38. To test its wheel, one casino records the results of 3800 plays finding 1890 reds numbers.Is that too many reds. Or chance variation?"

How do I compute this on R?

The correct size of a nickel is 21.21 millimeters. Based on that, the data can be summarized into the following table:

Based on this data: (give your answers to parts a-c as fractions, or decimals to at least 3 decimal places. Give your to part d as a whole number.)

a) The proportion of all children that drew the nickel too small is:   

Assume that this proportion is true for ALL children (e.g. that this proportion applies to any group of children), and that the remainder of the questions in this section apply to selections from the population of ALL children.

b) If 5 children are chosen, the probability that exactly 3 would draw the nickel too small is:

c) If 5 children are chosen at random, the probability that at least one would draw the nickel too small is:

d) If 120 children are chosen at random, it would be unusual if more than drew the nickel too small

Debt and financial risk: Tower Interiors has made the forecast of sales shown in the following table. Also given is the probability of each level of sales.

The firm has fixed operating costs of $75,200 and variable operating costs equal to 70%

of the sales level. The company pays $12,600 in interest per period. The tax rate is 40%.

a. Compute the earnings before interest and taxes​ (EBIT) for each level of sales.

b. Compute the earnings per share​ (EPS) for each level of​ sales, the expected​ EPS, the standard deviation of the​ EPS, and the coefficient of variation of​ EPS, assuming that there are

10,600 shares of common stock outstanding.

c. Tower has the opportunity to reduce its leverage to zero and pay no interest. This will require that the number of shares outstanding be increased to 15,900.

Repeat part ​(b​) under this assumption.

d. Compare your findings in parts ​(b​) and ​(c​)​, and comment on the effect of the reduction of debt to zero on the​ firm's financial risk.

From a survey of construction labor, the work duration (in number of hours) per day and the average productivity (percent efficiency) were recorded as follows:

SHOW ALL WORK

A. Determine the marginal probability distribution function (PDF) for X, the distribution of work duration and plot graphically on p_x (x) versus x for y = 6, 8, 10 and 12. Present p_x (x) in terms of relative frequencies of the observations.

B. Similarly, determine the marginal PDF for Y, representing the distribution of productivity.

C. If the work duration per day is 10 hr, what is the probability that the average productivity will be 85%?