Suppose a geyser has a mean time between eruptions of 71 minutes.Let the interval of time between the eruptions be normally distributed with standard deviation 24 minutes.

Complete parts ​(a) through ​(e) below.

​(a) What is the probability that a randomly selected time interval between eruptions is longer than 83 ​minutes?

The probability that a randomly selected time interval is longer than 83 minutes is approximately ____

​ (Round to four decimal places as​ needed.)

​(b) What is the probability that a random sample of 8 time intervals between eruptions has a mean longer than 83 ​minutes?

The probability that the mean of a random sample of 8 time intervals is more than 83 minutes is approximately ______

​(Round to four decimal places as​ needed.)

​(c) What is the probability that a random sample of 24 time intervals between eruptions has a mean longer than 83​ minutes?

The probability that the mean of a random sample of 24 time intervals is more than 83 minutes is approximately ____

​(Round to four decimal places as​ needed.)

​(d) What effect does increasing the sample size have on the​ probability? Provide an explanation for this result. Fill in the blanks below.

If the population mean is less than 83 ​minutes, then the probability that the sample mean of the time between eruptions is greater than

83 minutes (________________)because the variability in the sample mean(___________)as the sample size (_____________)

​(e) What might you conclude if a random sample of 24 time intervals between eruptions has a mean longer than 83 ​minutes? Select all that apply

A.The population mean is71​,and this is an example of a typical sampling result.

B.The population mean is 71​,and this is just a rare sampling.

C.The population mean may be greater than 71

D.The population mean must be more than 71​,since the probability is so low.

E.The population mean cannot be 71​,since the probability is so low.

F.The population mean must be less than 71 since the probability is so low.

G.The population mean may be less than 71

Suppose a geyser has a mean time between eruptions of 82 minutes.

Let the interval of time between the eruptions be normally distributed with standard deviation 23 minutes.

Complete parts ​(a) through ​(e) below.

​(a) What is the probability that a randomly selected time interval between eruptions is longer than 93 ​minutes?The probability that a randomly selected time interval is longer than 93 minutes is approximately _______.

​(Round to four decimal places as​ needed.)

​(b) What is the probability that a random sample of 9 time intervals between eruptions has a mean longer than 93 ​minutes?The probability that the mean of a random sample of 9 time intervals is more than 93 minutes is approximately ________.

​(Round to four decimal places as​ needed.)

​(c) What is the probability that a random sample of 18 time intervals between eruptions has a mean longer than 93 ​minutes?The probability that the mean of a random sample of 18 time intervals is more than 93 minutes is approximately ________.

​(Round to four decimal places as​ needed.)

​(d) What effect does increasing the sample size have on the​ probability? Provide an explanation for this result. Fill in the blanks below.

If the population mean is less than 93 ​minutes, then the probability that the sample mean of the time between eruptions is greater than 93 minutes _________because the variability in the sample mean _________ as the sample size _______.

​(e) What might you conclude if a random sample of 18 time intervals between eruptions has a mean longer than 93 ​minutes? Select all that apply.

A.The population mean must be more than 82​, since the probability is so low.

B.The population mean may be greater than 82.

C.The population mean cannot be 82​, since the probability is so low.

D.The population mean must be less than 82​, since the probability is so low.

E.The population mean is 82​, and this is just a rare sampling.

F.The population mean is 82​, and this is an example of a typical sampling result.

G.The population mean may be less than 82

1) Many Americans use savings bonds to supplement retirement funds or to pay for qualified higher-education expenses. The U.S. Treasury even sells savings bonds online. Approximately one in every six Americans owns savings bonds. Suppose four Americans are randomly selected.

a) What is the probability that all own savings bonds?

b) What is the probability that none own savings bonds?

c) What is the probability that exactly two of the four own savings bonds (hint: need to think about how many arrangements there are)?

2) A friend who works in a big city owns two cars, one small and one large. Seventy-five percent of the time he drives the small car to work, and twenty-five percent of the time he drives the large car. If he takes the small car, he usually has little trouble parking, and is at work on time with probability 0.8. If he takes the large car, he is at work on time with probability 0.5. Drawing a tree diagram would be helpful.

a) What is the probability your friend arrives at work on time?

b) Given that he was on time on a particular morning, what is the probability that he drove the small car?

c) Are driving the small car and showing up to work on time independent or dependent events? Show mathematically how you know.

3) Suppose that in a survey of a large, random group of people, 17% are found to be smokers. Suppose further that 8% of the smokers and 1% of the non-smokers died of lung cancer. Drawing a tree time would be helpful.

a) What is the probability that a randomly selected person is a smoker and died of lung cancer?

b) What is the probability that a randomly selected person is a smoker or died of lung cancer?

c) What is the probability that a randomly selected person dies of lung cancer?

d) Given that a person died of lung cancer, what is the probability they were a smoker?

e) Are having lung cancer and being a smoker mutually exclusive? Show mathematically how you know.

f) Are having lung cancer and being a smoker independent? Show mathematically how you know.

1) A case of 24 cans contains 1 can that is contaminated. Three cans are to be chosen randomly for testing. How many different sets of 3 cans could be selected?

2) A state’s license plate has 6 positions, each of which has 37 possibilities (letter, integer, or blank). If someone requests a license plate with the first three positions to be BMW how many different license plates would satisfy this request?

3) The U.S. Census Bureau reports that 35% of adults attend a sporting event each year. What are the odds a randomly selected adult in the U.S. attended a sporting event last year?

4) You have to go to 5 different buildings on campus to turn in assignments. How many different orders could you follow when visiting the 5 buildings?

5) A casino in Las Vegas showed that the odds of the Minnesota Twins beating the Detroit Tigers in a baseball game as 4:7. What is the probability the Minnesota Twins will win the game? 6) John and Jane are married. The probability that John watches a certain television show is 0.4. The probability that Jane watches the show is 0.5. The probability that John watches the show, given that Jane does is 0.70. a) Find the probability that both John and Jane watch the show. b) Do John and Jane watch the show independently of each other? Justify your answer. c) Find the probability that either John or Jane watches the show.

7) The U.S. Census Bureau reports that 90.4% of adults aged 25 and over who are employed have graduated from high school and 34.0% of adults aged 25 and over who are employed have graduated from college. Assume that an adult aged 25 and over who has graduated from college also graduated from high school. a) What is the probability an adult aged 25 and over who is employed did not graduate from high school. b) What is the probability an adult aged 25 and over who is employed that graduated from high school also graduated from college? c) What is the probability an adult aged 25 and over who is employed that graduated from high school did not graduate from college? d) Are the events H (Employed adult aged 25 and over who graduated from high school) and C (Employed adult aged 25 and over who graduated from college) independent?

8) A survey of 400 undergraduate college students was conducted to study their views on government and the economy. The Survey worksheet of the HW1 data workbook on Moodle contains each student’s class standing and response to question 7 - which read “The job market will be better when I graduate than when I started college”. a) Construct a contingency table that has one row for each class standing and one column for each response. b) What is the probability a survey respondent is in their sophomore year? What type of probability is this? c) What is the probability a survey respondent Strongly Agrees with Question 7? What type of probability is this? d) What is the probability a sophomore survey respondent Strongly Agrees with Question 7? What type of probability is this? e) What is the probability a survey respondent is a Freshman who Disagrees with question 7? What type of probability is this? f) Are class standing and response to question 7 independent? Why?

: In this question we are going to return to the wonderful island of Alleybowlia where the inhabitants absolutely love bowling. Remember, that the island boasts one of the best bowling alleys of its continent and all citizens go play in the alley all weekend long. An entrepreneur in a neighbouring island has figured out a new way of producing super-smooth bowling balls (SSBB), which are supposed to guarantee plenty of strikes (which is a good thing in bowling). As a shipment of SSBB is arriving on the island, the citizens are busy figuring out how much they are willing to pay for them. The following table lists the citizens’ willingness to pay for their first, second and possibly third SSBB.

For instance, citizen A is willing to pay $500 for her first SSBB, $340 for the second and $130 for the third. In contrast, consumer B is not willing to pay anything for a third SSBB since she only needs or wants two.

A. Suppose the boat arrives and there are only seven SSBBs available for sale. Assume that it has cost $200 to produce and ship each of the seven SSBBs.

1. What is the range of prices compatible with market equilibrium?

2. Pick the highest market equilibrium price and calculate consumer surplus.

3. What is the producer surplus at the highest market equilibrium price?

4. What is total surplus at the highest market equilibrium price?

5. What is total surplus at the lowest market equilibrium price?

B. Now assume instead that the cost of shipping and producing each ball is $350, and any quantity can be produced.

6. What is the equilibrium price and quantity in this case?

7. Calculate consumer surplus, producer surplus and total surplus.

5.2. Recall, again, that the time to first pruning of basil plants is known to be normally distributed with an average of µ = 35 days and a standard deviation of σ = 3 days. This term, n another l ab with a stable environment where no construction i s going on, students i n Kathleen’s class are trying a new fertilizer combination on their standard sweet basil plants. They are interested in whether this new fertilizer is improving (decreasing) the average number of days to first pruning for their basil plants. 36 randomly chosen students observed that the average time to first pruning for their plants was x¯ = 34 days with a standard deviation of s = 2.4 days, and that their sample data looks fairly bell shaped. What is the probability of observing a time of first pruning of 34 days or less if nothing has changed from the old number of days to first pruning that was the norm? Does it appear that the new fertilizer combination is decreasing the number of days to first pruning?

a. If you wish to test whether there is merit to the supposition that this new fertilizer is the “ "cat's meow” and is helping the plants to grow faster, what null and alternative hypothesis would be of interest here? HINT: This test will have a left sided alternative.

c. State the z-test statistic value (from MINITAB).

d. Write the p-value statement (by hand) and its value (from MINITAB)

e. Does it appear that the new fertilizer is decreasing the number of days to first pruning, on average? Why or why not? Test with a level of significance of 5%.

g. State the t-test statistic value (from MINITAB) and the degrees of freedom (find by hand).

h. Write the p-value statement (by hand) and its value (from MINITAB)

i. For the 5% significance level, do you have significant evidence that the new fertilizer is decreasing the number of days to first pruning, on average? Why or why not?

Hi, I am doing up my homework on mathematics and here are some questions. I want to cross-reference my answers thank you. Decide if the statements below are True or False. Please include some rough workings for me to understand:

(1) Mr. Tan borrowed $500,000 from Bank XYZ at 5% annual interest to be repaid monthly over 20 years. The amount that he pays back to XYZ each month is between $3000 to $3500.

(2) Continuing from (1): after 15 years, Mr. Tan still owing the bank between $120,000 to $160,000.

(3) 8 persons can sit at a round table with 10 seats 9!/2 ways.

(4) 8 persons sit at a round table with 10 seats so that there is exactly one person between the two empty seats in 8! ways.

(5) On a square grid, you are allowed to go only east (i.e., horizontally to the right) or north (i.e., vertically upwards), moving 1 step at a time. The number of ways (i.e., the number of such paths) by which you can go from (3,3) to (5,5) is8 3.

(6) The number of ways in which 10 identical red balls and 7 identical blue balls can be arranged in a line is17 7.

(7) The sumP2019 k=0 2k is an even number.

(8) According to Benfords law, the probability of 5 being the leading digit of a long list of positive integers (such as the population of various cities) is 0.0969 (to 4 decimal places).

(9) Three fair dice are thrown. The expected value of the total score obtained is 10.5

(10) If the expected number of heads in 5 independent tosses of a coin is 3, then the coin must be fair.

1.   A researcher conducted a survey on a university campus for a sample of 64 seniors. The research reported that seniors read an average of 3.12 books in the prior academic semester, with a standard deviation of 2.15 books. Determine the probability that the sample mean is:
   a) above 3.45
   b) between 3.38 and 3.58
   c) below 2.94
2.   Al Gore, the Democratic candidate for President of the USA in the 2000 election, believes that the proportion of voters who will vote for a Democrat candidate in the year 2004 presidential elections is 0.65. A sample of 500 voters is selected at random.
a.   Assume that Gore is correct and p = 0.65. What is the sampling distribution of the sample proportion ? Explain.
b.   Find the expected value and the standard deviation of the sample proportion .
c.   What is the probability that the number of voters in the sample who will vote for a Democrat presidential candidate in 2004 will be between 340 and 350?
3.   A random sample of 10 waitresses in Iowa City, Iowa revealed the following hourly earnings (including tips):

$19   18   15   16   18   17   16   18   20   14

If the hourly earnings are normally distributed with a standard deviation of $4.5, estimate with 95% confidence the mean hourly earnings for all waitresses in Iowa City.
4.   The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 15. A random sample of 400 salespersons was taken and the mean number of cars sold annually was found to be 75. Find the 95% confidence interval estimate of the population mean. Interpret the interval estimate.
5.   Suppose that in a large city, the annual income of real estate agents is normally distributed with a standard deviation of $7,500. A random sample of 16 real estate agents reveals that the mean annual income is $52,000. Determine the 99% confidence interval estimate of mean annual income of all real estate agents in the city.
6.   A medical statistician wants to estimate the average weight loss of people who are on a new diet plan. In a preliminary study, he guesses that the standard deviation of the population of weight losses is about 10 pounds. How large a sample should he take to estimate the mean weight loss to within 2 pounds, with 90% confidence?

Design your own experiment to demonstrate the probability of states using objects of your choice. Use Probability of States as a guide for experimental design.