If a random sample of 100 items is taken from a population in which the proportion of items having a desired attribute is p=0.45, what is the probability that the proportion of successes in the sample will be less than or equal to 0.49

The probability will be ____

A study of 100 students in a local university gave the average GPA to be 3.1 with a standard deviation of.5. The same study revealed that in this sample, 20% are out of state students.

1. The lower bound, correct up to 3 decimal places for a 92% confidence interval for the actual GPA of students in this university is

2. The lower bound, correct up to 3 decimal places of a 90% confidence interval for the true proportion of out of state students is

3. The lower bound, correct up to 3 decimal places, of a 95% confidence interval for the true GPA with a sample size of 20, a sample mean of 3.1 ad a standard deviation of 0.5 is

4. The exact number of students that need be surveyed for the true GPA to be estimated within .5 units with a 96% confidence

In a random sample of 100 audited estate tax​ returns, it was determined that the mean amount of additional tax owed was ​$3494 with a standard deviation of ​$2527. Construct and interpret a​ 90% confidence interval for the mean additional amount of tax owed for estate tax returns.

You are studying a population of 100 lizards that has two alleles at a locus for skin color, blue (B) and green (G). There are 30 individuals with the BB genotype, 30 individuals with the BG genotype, and 40 individuals with the GG genotype.

(a) What are the allele frequencies of B and G in the starting population? Show your calculations.

(b) Is this population in Hardy-Weinberg equilibrium? Show your calculations.

How many molecules are in a 100 mL container of gaseous oxygen if the pressure is 2.30x10^ -7 torr and the temperture is 1105 k?

b. How many grams of oxygen are in the container?

1. Discuss the fact that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Ashton Kutcher has been reported on several websites to have an IQ of 160.

a. What does it mean to have an IQ of 160?

b. What is the z-score of Ashton Kutcher’s IQ?

c. What proportion of people have an IQ score of more than 160?

d. Assuming there are about 323 million Americans, how many Americans have an IQ of over 160?

e. Do you think these websites are correct about the IQ of Ashton Kutcher?

2. Discuss the following populations and decide if the population is approximately normally distributed.

a. The lengths of the longest hair on the heads of female VVC students.

b. The numbers of hats worn by VVC students during a given school day (M-Th).

c. The amounts of liquid in all 8oz soda cans on store shelves in the United States.

d. The amounts of money spent on jeans in 2016 for every resident of Beverly Hills, CA.

e. The lifespans of all dry erase markers that are currently in the Technology Building. (The length in time from when they are taken out of the package to when they are thrown away.)

Then, have each group come up with an example of a population that is approximately normally distributed, and discuss.

Suppose 90% of a sample of 100 randomly selected homes in Town A and 80% of a sample of 50 randomly selected homes in Town B rely on the public water supply for drinking water. Compute the test statistic for a hypothesis test to compare the population proportion of homes that rely on the public water supply for drinking water in Town A to the proportion in Town B. Assume that the conditions for a hypothesis test for the difference between the population proportions are met. Round your answer to two decimal places.

z score=??

Show the observed probabilities for 10 trials and 100 trials for a game of Rock / Paper / Scissors with the probability of each outcome being equal.

1. The standardized IQ test is described as a normal distribution with 100 as the mean score and a 15-point standard deviation.

a. What is the Z-score for a score of 150?

b. What percentage of scores are above 150?

c. What percentage of scores fall between 85 and 150?

d. What does it mean to score in the 95th percentile?

e. What is the score that corresponds to being in the 95th percentile?

2. A friend wants to learn about the average weekly take-home pay for an Uber driver in Arkansas. After asking Uber to tell her this, they denied her request saying if she wanted to find out she would need to ask people on her own. With the help of a local ride-sharing driver organization, she obtained what she believes to be a list of all Uber drivers in the state of Arkansas. She asks you for help in figuring out what to do next.

a. What is the population and parameter of interest?

b. What is the sample statistic of interest?

3. After looking at the list you find out that there are 40,000 drivers listed. She doesn’t have money to contact 40,000 drivers in her research budget. Instead, she can talk to about 1,000. In your email reply to her, you tell her that it shouldn’t be a problem that she can only talk to about 1,000 drivers, assuming you select them the right way  

a. What is the “right way” to select the drivers? Make sure to explain what the “right way” is, not just provide the term.

b. Why do you tell her that it’s not a problem if you select them the right way? That is, what explanation do you give to her to explain that she can learn what she wants with the small sample? Your explanation should include the basics of probability sampling, sampling distributions, and the central limit theorem.

4. Agreeing to move forward with the research, she asks you to explain the different ways of developing a sample. She also mentioned she was interested in comparing the differences in earnings between women who are mothers, women who are not, and men.

a. How would you describe simple random sampling to her, and how would you construct a simple random sample from these data?

b. Describe systematic sampling to her and describe how you might construct such a sample from these data.

c. Describe stratified random sampling to her, how it might be useful for comparing the earnings between women who are mothers, those who aren’t, and men, and how you might construct such a sample from these data.

5. If the population parameter is $400, with a standard deviation of $100. What percentage of your potential sample statistics from the population of size 1,000 will fall between a value of $393.68 and $406.32?

A makeup test is given and the average (μX) score out of 100 was 85.0, with a SD (σX) of 3.0. Assuming a normal distribution, find the dividing line (test scores) between the A's, B's, C's, D's, and E's. This time the highest 6% will be the A's, the next 16% B's, the next 26% C's, the next 36% D's.