Suppose we have the following pdf for the random variable X

f(x) ={x 0<=x<=1

c/x^2 1<=x<= infinity

0 otherwise

}

(a) 2 points Find the value c such that f(x) is a valid pdf.

(b) 3 points Find the cdf of X.

(c) 1 point Find the 75th percentile of X.

In a random sample of 7 residents of the state of Texas, the mean waste recycled per person per day was 2.7 pounds with a standard deviation of 0.72 pounds. Determine the 99% confidence interval for the mean waste recycled per person per day for the population of Texas. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

T or F

The main reason a research uses a t-test instead of a z-test is when little is known about population (mean and standard deviation).

Values in the t‐table are not actually listed by sample size but by degrees of freedom (df).

A 90 percent confidence level is equivalent to an alpha level of 0.10

The critical value of t‐table for a study with 6 participants with alpha set @ .1 one tail is 1.711

Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution. 95 176 134 100 75 94 116 100 85 (a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviation s. (Round your answers to one decimal place.) x = thousand dollars s = thousand dollars (b) Find a 90% confidence interval for the population average startup costs μ for candy store franchises. (Round your answers to one decimal place.) lower limit thousand dollars upper limit thousand dollars

Two machines are used for filling glass bottles with a soft-drink beverage. The filling processes have known standard deviations s1=0.010 liter and s2=0.015 liter, respectively. A random sample of n1=25 bottles from machine 1 and n2=20 bottles from machine 2 results in average net contents of x1=2.04 liters and x2=2.07 liters.

(a) Test the hypothesis that both machines fill to the same net contents, using alpha=.05. What are your conclusions?

(b) Find the P-value for this test.

(c) Construct a 95% confidence interval on the difference in mean fill volume.

In the inspection of tin plate produced by a continuous electrolytic process, 0.2 imperfection is spotted per minute on average. Find the probabilities of spotting.

(a) one imperfection in 3 minutes.

(b) at least two imperfections in 5 minutes.

Personnel in a consumer testing laboratory are evaluating the absorbency of paper towels. They wish to compare a set of Walmart generic brand towels to similar group of BOUNTY name brand towels. For each brand they dip one towel into a tub of fluid, allow the paper to drain back into the vat for two minutes, and then determine the amount of liquid the paper has taken up from the vat. A random sample of 9 Walmart generic brand towels has a mean of 6.44 milliliters with a standard deviation of 3.32 milliliters. A random sample of 12 Bounty Brand towels hand sample mean of 9.42 milliliters with a standard deviation of 1.621 milliliters. Use the .10 significance to test if there is a difference in the mean amount of liquid absorbed by the two paper towels. Assume the population standard deviations are not equal.

1. State the Null and Alternate Hypothesis(H0, H1).

2. Determine the level of significance.

3. Determine the test statistic. (z or t)

4. State the decision rule.(Reject H0 if)

5. Conduct the test and make a decision.(Include Formula and show all work)

6. Interpret the results.

"PLEASE SHOW ALL WORK WITH THE CORRECT ANSWERS"

Thanks!

Construct a

99​%

confidence interval of the population proportion using the given information.

x=120, n=200

The lower bound is

-----

The upper bound is

------

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

Students of a large university spend an average of $6 a day on lunch. The standard deviation of the expenditure is $2. A simple random sample of 81 students is taken. 1. What is the probability that the sample mean will be at least $5.25? 2. What is the probability that the sample mean will be at least $6.50? 3. What is the range of money spent by people who fall within one standard deviation of the mean? 4. Kelsey spent $12 on her lunch today. Explain to her, in terms of the normal distribution curve and standard deviation, why her purchase is not very typical.

The manager of the Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of future weekend guest bills to test the manager’s claim. a. Which form of the hypotheses should be used to test the manager’s claim? b. What conclusion is appropriate when ?0 cannot be rejected? c. What conclusion is appropriate when ?0 can be rejected? d. What is the Type I and Type II errors in this situation?

Consider the data set.

• 2,
• 3,
• 4,
• 6,
• 8

(a)

Find the range. (Enter an exact number.)

(b)

Use the defining formula to compute the sample standard deviation s. (Enter a number. Round your answer to two decimal places.)

(c)

Use the defining formula to compute the population standard deviation σ. (Enter a number. Round your answer to two decimal places.)

Three barbers work at a barbershop. Based on estimations, the barbershop is idle 1 time out of 15; 2/15 of the time there is one customer; 3 times out of 15 there are two customers; and 4/15 of the time, there are three customers. Each customer yields a net revenue of 10 dollars.

Let X be a random variable defined as the number of customers

a) Determine the probability distribution of X

b) Determine the cumulative distribution function of X

c) Calculate the probability that: i) All three barbers are working. ii) At least one of the barbers is working

The distribution of the prices of new phone is positively skewed with a long tail to the right, in a random sample of people who have purchased a new phone, a mean and standard deviation price of a new phone is reported to be $400 and $50 respectively.

What is the standard deviation of price of a new phone costing $500 in this distribution? Please indicate the standard deviation with the sign (negative and positive) and in the unit as “s”

Based on historical data, your manager believes that 34% of the company's orders come from first-time customers. A random sample of 71 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.32?

Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer =0.3555 was wrong

B.Based on historical data, your manager believes that 32% of the company's orders come from first-time customers. A random sample of 138 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.21 and 0.35?

Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

Answer = 0.7736 was the wrong answer (Enter your answer as a number accurate to 4 decimal places.)

C.You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 90% confident that you esimate is within 2.5% of the true population proportion. How large of a sample size is required?

n =
Do not round mid-calculation. However, use a critical value accurate to three decimal places.