Customers arrive at a local ATM at an average rate of 14 per hour. Assume the time between arrivals follows the exponential probability distribution. Determine the probability that the next customer will arrive in the following time frames.

​a) What is the probability that the next customer will arrive within the next 2 ​minutes?

​b) What is the probability that the next customer will arrive in more than 15 ​minutes?

​c) What is the probability that the next customer will arrive between 8 and 13 ​minutes?

1. Ross White’s machine shop uses 2,500 brackets during the course of a year, and this usage is relatively constant throughout the year. These brackets are purchased from a supplier 100 miles away for $15 each, and the lead time is 2 days. The holding cost per bracket per year is $1.50 (or 10% of the unit cost), and the ordering cost per order is $18.75. There are 250 working days per year.

   1. What is the EOQ?

   2. Given the EOQ, what is the average inventory? What is the annual inventory holding cost?

   3. In minimizing cost, how many orders would be placed each year? What would be the annual ordering cost?

   4. Given the EOQ, what is the total annual inventory cost (including purchase cost)?

   5. What is the time between orders?

   6. What is the ROP?

A medical researcher claims that the proportion of people taking a certain medication that develop serious side effects is 12%. To test this claim, a random sample of 900 people taking the medication is taken and it is determined that 93 people have experienced serious side effects. . The following is the setup for this hypothesis test: H0:p = 0.12 Ha:p ≠ 0.12 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places. The following table can be utilized which provides areas under the Standard Normal Curve:

Air-USA has a policy of booking as many as 21 persons on an airplane that can seat only 19. (Past studies have revealed that only 85% of the booked passengers actually arrive for the flight.)

Find the probability that if Air-USA books 21 persons, not enough seats will be available. prob = ?

Is this probability low enough so that overbooking is not a real concern for passengers if you define unusual as 5% or less?

yes, it is low enough not to be a concern

no, it is not low enough to not be a concern

What about defining unusual as 10% or less?

yes, it is low enough not to be a concern

no, it is not low enough to not be a concern

Please share your thoughts about the application of statistics in today’s business? Also, what are some of the good examples as when / how you would apply statistics in business?

Suppose just over 2500 cell phones are produced at a factory today. Management would like to ensure that the phones' display screens meet their quality standards before shipping them to retail stores. Since it takes about 10 minutes to inspect an individual phone's display screen, managers decide to inspect a sample of 50 phones from the day's production.

(a) Explain why it would be difficult for managers to inspect an SRS of 50 phones produced today.

(b) An eager employee suggests that it would be easy to inspect the last 50 phones that were produced today. Obviously, this employee never took a stats class! Explain why this is not a good method.

(c) Another employee that did take a stats class recommends inspecting every 50th phone produced today. What sampling method are they using?

Question (statistics) (Data below) (to be done with EVIEWS or any data processor)

Millions of investors buy mutual funds, choosing from thousands of possibilities. Some funds can be purchased directly from banks or other financial institutions (direct) whereas others must be purchased through brokers (broker), who charge a fee for this service. A group of researchers randomly sampled 50 annual returns from mutual funds that can be acquired directly and 50 from mutual funds that are bought through brokers and recorded their net annual returns (NAR, %), which are the returns on investment after deducting all relevant fees.1 These data are saved in the two columns of the a1.xlsx spreadsheet labelled as Purchase and NAR, respectively. Import these data to EViews.

(a) Are Purchase and NAR qualitative or quantitative variables? If they are qualitative, are they ranked or unranked? If they are quantitative, are they discrete or continuous? What are their levels of measurement? Explain your answers.

(b) Use EViews to obtain the basic descriptive statistics for NAR. Briefly describe what they tell you about the net annual returns from mutual funds.

(c) Using the relevant statistics from part (b), estimate with 90% confidence the mean net annual returns. What assumption do you have to make to perform this task?

(d) Using the relevant statistics from part (b), briefly evaluate whether the assumption needed for the confidence interval in (c) is likely violated.

(e) In general, we can conduct hypothesis tests on a population central location with EViews by performing the (one sample) t-test, the sign test or the Wilcoxon signed ranks test.2 Suppose we would like to know whether there is evidence at the 5% level of significance that the population central location of NAR is larger than 5%. Depending on your answer in part (d), which test(s) offered by EViews would be the most appropriate this time? Explain your answer by considering the conditions required by these tests.

(f) Perform the test you selected in part (e) above with EViews. Do not forget to specify the null and alternative hypotheses, to identify the test statistic, to make a statistical decision based on the p-value, and to draw an appropriate conclusion. If the test relies on normal approximation, also discuss whether this approximation is reasonable this time.

(g) Perform the other tests mentioned in part (e). Again, do not forget to specify the null and alternative hypotheses, to identify the test statistics, to make statistical decisions based on the p-values, and to draw appropriate conclusions. Also, if the tests rely on normal approximation, discuss whether these approximations are reasonable this time.

(h) Compare your answers in parts (f) and (g) to each other. Does it matter in this case whether the population of net returns is normally, or at least symmetrically distributed or not? Explain your answer.

Data

A psychologist has designed a questionnaire to measure individuals' aggressiveness. Suppose that the scores on the questionnaire are normally distributed with a standard deviation of 80 . Suppose also that exactly 10% of the scores exceed 750 . Find the mean of the distribution of scores. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place 7. suppose that the antenna lengths of woodlice are approximately normally distributed with a mean of 0.2 inches and a standard deviation of 0.05 inches. What proportion of woodlice have antenna lengths that are less than 0.15 inches? Round your answer to at least four decimal places. 8. In a certain city of several million people, 6.8% of the adults are unemployed. If a random sample of 240 adults in this city is selected, approximate the probability that at most 14 in the sample are unemployed. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps. (If necessary, consult a list of formulas.)

In certain drug trial, 10 subjects who received a placebo reported headaches, while 30 subjects who received a placebo reported no headaches. Of the subjects taking a new drug, 20 reported headaches, while 30 did not. a) Display this information in a contingency table, including all totals. b) What percentage of participants in the trial reported headaches? c) What percentage of new-drug takers reported headaches? d) What percentage of placebo takers reported headaches?

a) Draw a diagram to show a standard Normal distribution and shade in the regions between (µ–3(sigma)) and (µ+(sigma)). Find the approximate percentage of the population that would have values in this region. b) A researcher has found that among many mice in given maze the average time to complete the circuit is 10 minutes. The times were normally distributed with a standard deviation of 3 minutes. Find: i) the approximate proportion of mice that completed the maze in less than 4 minutes, ii) the probability that a random mouse takes more than 15 minutes to complete the maze, iii) the time to complete the maze below which are the fastest 5% of mice, and iv) the first quartile of the times to complete the maze

Use the following stem-and-leaf display of the ages of 10 persons.

1 | 2 4 4

2| 1 1 2 6 9

3| 2

4|

5 | 8

a) Find the mean and mode of the ages. b) By hand, find the five-number summary of the ages. c) Find the range and interquartile range of the ages. d) Provide a dot plot of the ages.

A shoe salesman wants to see if his female customers have a preference in the color of shoe purchased. He notes the color preferences of 100 randomly selected customers. The results: Black=32, Brown=27, Red=15, Navy =13 White =13

• Consider a t distribution with 7degrees of freedom. Compute

  P(t+≥ −1.05) Round your answer to at least three decimal places.

• Consider a t distribution with 11degrees of freedom. Find the value of c such that

  =P(-c < t < c)= 0.95 Round your answer to at least three decimal places.

• P(t≥ -1.05)=

• c=

Is smoking during pregnancy associated with premature births? To investigate this question, researchers selected a random sample of 131 pregnant women who were smokers. The average pregnancy length for this sample of smokers was 262 days. From a large body of research, it is known that length of human pregnancy has a standard deviation of 16 days. The researchers assume that smoking does not affect the variability in pregnancy length. Find the 95% confidence interval to estimate the length of pregnancy for women who smoke. (Note: The critical z -value to use, z c , is: 1.960) ( , ) Your answer should be rounded to 3 decimal places.

Let X be the weight of a randomly selected 10oz bag of chips. Suppose that X has a normal distribution with a mean of 10.2 and standard deviation of .05. Find the weight of x* so that 95% of all 10oz bags have a weight of at least x*.