Customers arrive in a certain shop according to an approximate Poissonprocess on the average of two every 6 minutes.

(a) Using the Poisson distribution calculate the probability of two or more customersarrive in a 2-minute period.

(b) Consider X denote number of customers and X follows binomial distribution withparametersn= 100. Using the binomial distribution calculate the probability oftwo or more customers arrive in a 2-minute period.

(c) Let Y denote the waiting time in minutes until the first customer arrives. (i) Whatis the pdf ofY? (ii) Findq1=π0.75

(d) Let Y denote the waiting time in minutes until the first customer arrives. What isthe probability that the shopkeeper will have to wait more than 3 minutes for thearrival of the first customer ?

(e) What is the probability that shopkeeper will wait more than 3 minutes before bothof the first two customers arrive?

briefly describe the company’s franchise structure which you researched. Suggest one (1) way in which the company could improve its franchise structure to make it more attractive to potential customers.

Please discuss using twitter and LinkedIn as media channels for a conference about a start-up company, to create meaningful touch points with targeted customers throughout their journey and explain their significance in the service experience.

Suppose you know that a company’s stock currently sells for $74 per share and the required return on the stock is 9.9 percent. You also know that the total return on the stock is evenly divided between a capital gains yield and a dividend yield. It's the company’s policy to maintain a constant growth rate in its dividends. What is the current dividend per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Hint: First, compute the current dividend yield. Then, use that to compute the next dividend paid (in dollars per share). Then, using the constant dividend growth rate, compute the last dividend paid. The dividend is equal to the dividend yield multiplied by the stock price. Remember that the current stock price reflects future dividends, starting with D1, where D1 = D0(1 + g).

A person of mass 74 kg stands at the center of a rotating merry-go-round platform of radius 3.5 m and moment of inertia 880 kg⋅m2 . The platform rotates without friction with angular velocity 0.90 rad/s . The person walks radially to the edge of the platform.

Calculate the angular velocity when the person reaches the edge.

Calculate the rotational kinetic energy of the system of platform plus person before and after the person's walk.

Each "2p" electron deep inside a Tungsten atom is influenced mostly by 74 protons in the nucleus (treat as a point), and the 4 electrons (treat as shells around the nucleus) which are interior to it (2 in 1s and 2 in 2s). How fast does one of these "2p" electrons need to be moving, to travel around a circular orbit with radius 3.158[pico-meter]? {m_e=0.911E−30[kg]}

1. A random sampling of 60 pitchers from the National League and 74 pitchers from the American League showed that 38 National and 36 American League pitchers had E.R.A's below 3.5.

Find the test statistic that would be used to test the claim that the proportion of the NL pitchers with E.R.A. below 3.5 is higher than the proportion of the AL pitchers with similar stats.

Round your answer to three decimal places.

2. Two independent samples are randomly selected and come from populations that are normal. The sample statistics are given below:

n1 = 47 n2 = 52

1 = 24.2 2 = 18.7

s1 = 5.0 s2 = 5.6

Find the standardized test statistic t to test the hypothesis that μ1 = μ2. Round your answer to three decimal places.

A certain tennis player makes a successful first serve 74​% of the time. Suppose the tennis player serves 110 times in a match.​ What's the probability that she makes at least 86 first​ serves?

Suppose you run a regression containing observations for each of the 74 kinds of cars released in 1978 in the United States, and you regress price (in dollars) on weight (in pounds). You get the following results:
ˆ β0 is -6.71, with SE 1174.4. ˆ β1 (slope coefficient on weight) is 2.04 with SE .377.
• (a) Say, in words, what the slope coefficient means in this case, without taking a stand on causality.

• (b) Suppose I give you the following information: the sum of squares total is roughly equal to 635 million, and the sum of squares explained is equal to 185 million. Please report the R2 and the correlation coefficient between price and weight.

• (c) Use your regression model to predict what the price would be for a car that weighs 3000 pounds.

• (d) Use the SER to add uncertainty and make this prediction an interval. • (5 points) Build a 95% confidence interval for the slope coefficient and report the p-value for comparing it to 0. Interpret your results.