​​​​​​​Please post the work so I can understand the process :) Thanks!

1. Telephone calls arrive at the Global Airline reservation office in Louisville according to a Poisson distribution with a mean of 1.6 calls per minute:

a. What is the probability of receiving exactly one call during a one-minute interval?

b. What is the probability of receiving at most 2 calls during a one-minute interval?

c. What is the probability of receiving at least two calls during a one-minute interval?

d. What is the probability of receiving exactly 4 calls during a five-minute interval?

Students will examine and interpret 14 variables from a random sample of 1450 birth records taken by the North Carolina State Center for Health and Environmental Statistics in 2001, and communicate the information by describing the data set, both graphically and numerically, in the form of a PowerPoint presentation.

Question 1) Propose three other variables you would like to investigate in regard to weight of the mother. Write the explicit question you would ask the mother prior to delivery and in writing explain why you want to know that information.

The variables in this study are:

Suppose the population average amount of dog biscuits in a bag is 40 pounds with a standard deviation of 6 pounds. A simple random sample of 64 bags is selected. A)What is the probability the sample mean weight will be more than 39 pounds? b)What is the probability the sample mean weight will be within 1.5 pounds of the population mean c) 50% of the time the sample mean weight is less than what?

1. The effects of mind-altering products (alcohol intake and medication) on aggressive driving are studied in a group of individuals who drink regularly and take prescription medication. Thirty individuals are assigned based on to their respective groups: either a placebo group (those who do not drink or take medication), medication group (whose members regularly take medication), and alcohol group (whose members regularly drink) who will receive an ounce of alcohol 30 minutes before the driving simulation test is given. The dependent variable is the number of crashes during the 5-minute driving simulation. Determine whether or not there is a significant difference with at least one group. If you reject the null hypothesis, tell what it means in the context of the problem. Include the statistical sentence.

(Use p=.05 or 5%).

Alcohol           Medication     Placebo

10                    7                      5

15                    7                      3

12                    5                      2

8                      8                      4

5                      10                    6                     

21                    13                    5

10                    12                    1

11                    11                    2

13                    11                    5

20                    15                    2

For the next 7 questions, please refer to the following information.

Mr. Cherry owns a gas station on a highway in Vermont. In the afternoon hours, there are, on average, 30 cars per hour passing by the gas station that would like to refuel. However, because there are several other gas stations with similar prices on the highway, potential customers are not willing to wait—if they see that all of the pumps are occupied, they continue on down the road.
The gas station has three pumps that can be used for fueling vehicles, and cars spend four minutes, on average, parked at a pump (filling up their tank, paying, etc.).

d. What is the probability that all three pumps are being used by vehicles?

• A. 0.1895
• B. 0.1650
• C. 0.1458
• D. 0.2105

e. How many customers are served every hour?

• A. 23.7
• B. 25.6
• C. 12.7
• D. 16.7

f. What is the utilization of the pumps?

• A. 0.63
• B. 0.83
• C. 0.53
• D. 0.73

g. How many pumps should it have to ensure that it captures at least 98 percent of the demand that drives by the station?

• A. 6
• B. 2
• C. 4
• D. 8

An article about the California lottery gave the following information on the age distribution of adults in California: 35% are between 18 and 34 years old, 51% are between 35 and 64 years old, and 14% are 65 years old or older. The article also gave information on the age distribution of those who purchase lottery tickets. The following table is consistent with the values given in the article. Suppose that the data resulted from a random sample of 200 lottery ticket purchasers. Based on these sample data, is it reasonable to conclude that one or more of these three age groups buys a disproportionate share of lottery tickets? Use a chi-square goodness-of-fit test with α = 0.05. (Round your answer to two decimal places.)

χ² =

P-value interval

p < 0.0010.001 ≤ p < 0.01    0.01 ≤ p < 0.050.05 ≤ p < 0.10p ≥ 0.10

The data  ---Select--- provide do not provide strong evidence to conclude that one or more of the three age groups buys a disproportionate share of lottery tickets.

RideShare offers short-term rentals of vehicles that are kept in small lots in urban neighborhoods with plenty of potential customers. With one lot, it has eight cars. The interarrival time of potential demand for this lot from its base of customers is 40 minutes. The average rental period is five hours. If a customer checks availability of vehicles in this lot online and finds that they are all rented for the desired time, the customer skips renting and finds alternative arrangements. However, because customers pay a monthly fee to subscribe to this service, RideShare does not want customers to be disappointed too often.

b. What is the implied utilization?

• A. 0.87
• B. 0
• C. 0.54
• D. 0.94

c. What is the capacity of the process (rentals per hour)?

• A. 3.6
• B. 1.6
• C. 2.6
• D. 4.6

d. What is the probability that all eight cars are rented at the same time?

• A. 0.207
• B. 0.107
• C. 0.307
• D. 0.407

All euros have a national image on the "heads" side and a common design on the "tails" side. Spinning a coin, unlike tossing it, may not give heads and tails with equal probabilities. Polish students spun the Belgian euro 259 times, with its portly king, Albert, displayed on the heads side. The result was 157 heads.

Test the hypothesis that the proportion of times a Belgian Euro coin spins heads equals 50% at alpha = 0.05 .

The test statistic is z =???

with P-value ??? . (Use three decimals on both.)

With Obesity on the rise, a Doctor wants to see if there is a linear relationship between the Age and Weight and estimating a person's Systolic Blood Pressure. Using that data, find the estimated regression equation which can be used to estimate Systolic BP when using Age and Weight as the predictor variable.

See Attached Excel for Data.

• A.

  Systolic BP = 31.73252234 + 0.965183151(Age) + 2.666383416(Weight)

• B.

  Systolic BP = 31.73252234 + 0.938835263(Age) + 0.309246373(Weight)

• C.

  Systolic BP = 31.73252234 + 0.984797135(Age) + 0.969825398(Weight)

• D.

  Systolic BP = 11.05638371+ 0.230153049(Age) + 0.120862651(Weight)

• Systolic BP	Age in Yrs.	Weight in lbs.
  132	52	173
  143	59	184
  153	67	194
  162	73	211
  154	64	196
  168	74	220
  137	54	188
  149	61	188
  159	65	207
  128	46	167
  166	72	217
  135	52	187
  148	61	189
  161	65	205
  126	45	161
  167	71	215

The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table.

(a) What is the probability that there is exactly one car and exactly one bus during a cycle?


(b) What is the probability that there is at most one car and at most one bus during a cycle?


(c) What is the probability that there is exactly one car during a cycle? Exactly one bus?

(d) Suppose the left-turn lane is to have a capacity of five cars and one bus is equivalent to three cars. What is the probability of an overflow during a cycle?


(e) Are X and Y independent rv's? Explain.

Yes, because p(x, y) = p_X(x) · p_Y(y).Yes, because p(x, y) ≠ p_X(x) · p_Y(y).    No, because p(x, y) = p_X(x) · p_Y(y).No, because p(x, y) ≠ p_X(x) · p_Y(y).

A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.

(a) Given that X = 1, determine the conditional pmf of Y—i.e., p_Y|X(0|1), p_Y|X(1|1), p_Y|X(2|1). (Round your answers to four decimal places.)

(b) Given that two hoses are in use at the self-service island, what is the conditional pmf of the number of hoses in use on the full-service island? (Round your answers to four decimal places.)

(c) Use the result of part (b) to calculate the conditional probability P(Y ≤ 1 | X = 2). (Round your answer to four decimal places.)
P(Y ≤ 1 | X = 2) =

(d) Given that two hoses are in use at the full-service island, what is the conditional pmf of the number in use at the self-service island? (Round your answers to four decimal places.)

The Gardner Theater, a community playhouse, needs to determine the lowest-cost production budget for an upcoming show. Specifically, they have to determine which set pieces to construct and which, if any, set pieces to rent from another local theater at a predetermined fee. However, the organization has only two weeks to fully construct the set before the play goes into technical rehearsals. The theater has two part-time carpenters who work up to 12 hours a week, each at $10 an hour. Additionally, the theater has a part-time scenic artist who can work 15 hours per week to paint the set and props as needed at a rate of $15 per hour. The set design requires 20 flats (walls), two hanging drops with painted scenery, and three large wooden tables (props). The number of hours required for each piece for carpentry and painting is shown below:

A researcher states that the time that urban preschool children between 3 and 5 years spend watching television per week has an average of 22.6 hours and a standard deviation of 6.1 hours. A market research company believes that the proclaimed mean is very small. To test their hypothesis, a random sample of 60 urban preschool children is taken and the time they spend watching television is measured, with parents registering it daily on a record sheet. If the weekly mean time spent watching television is 25.2 hours and the population standard deviation is assumed to be 6.1 hours, should the researchers' statement with an α value of 0.01 be rejected?

Because of the pandemic, Wegman’s wants to expedite their grocery services by reorganizing so that people do not have to spend as much time in their store each visit. They sample random customers to see how long they spend shopping at the store. After reorganizing, they measure how long those same customers take in the grocery store.

Your data show the following for a sample of 16 customers.

a. Wegmans hires you to determine how successful their reorganization was. Did the reorganization reduce the amount of time customers shop in the store? Set up, conduct, and interpret a hypothesis test to answer this question based on a Type-I error rate of 0.01.

b. The p-value for this test was found to be about 0.008, explain what that means.

c. What assumption do you need to make in order for this test to be valid? Be specific.