The heights of 1000 students are approximately normally distributed with a mean of 174.5centimeters and a standard deviation of 6.9 centimeters. Suppose 200 random samples ofsize 25 are drawn from this population and the means recorded to the nearest tenth of acentimeter. Determine

(a) the mean and standard deviation of the sampling distribution of ̄X;

(b) the number of sample means that fall between 171 and 177 cm .

Let X be a random variable following a continuous uniform distribution from 0 to 10. Findthe conditional probabilityP(X≥3|X <5.5).

2. Chebyshev’s theorem states that the probability that a random variableXhas a value atmost 3 standard deviations away from the mean is at least 8/9. Given that the probabilitydistribution of X is normally distributed with meanμand varianceσ2, find the exact value of

P(μ−3σ < X < μ+ 3σ)

1. In forest, the average number of maples was 20 trees/plot with a standard deviation of 7 trees/plot. If we take a sample of eight plots, what is the probability that the mean of this sample will be between 18 and 21?

2. Assuming the octane ratings are normally distributed, use the octane ratings data to construct a 95% confidence interval for the mean octane rating.

3. We want to test how accurate an optical character recognition (OCR) device is. We collect a sample of 500 handwritten words and find out that 440 were read correctly. Construct a 95% confidence interval for the population proportion.    

4. We want to see what proportion of seeds will germinate. We plant 200 seeds and see that 194 germinate. Construct a 95% confidence interval for the population proportion.

a) Zoey Enterprises manufactures solar engines for helicopters. Given the fuel savings available, new orders for 125 units have been made by customers requesting credit. The variable cost is $11,400 per unit, and the credit price is $13,000 each. Credit is extended for one period. The required return is 1.9 percent per period. If Zoey Enterprises extends credit, it expects that 30 percent of the customers will be repeat customers and place the same order every period forever, and the remaining customers will place one-time orders. Should credit be extended?

b) Now, assume that the probability of default is 15 percent. Should the orders be filled now? Assume the number of repeat customers is affected by the defaults. In other words, 30 percent of the customers who do not default are expected to be repeat customers.

Consider a diagnostic test for a hypothetical disease based on measuring the amount of a

certain biomarker present in blood. High levels of the biomarker are often found in individuals

with the disease, but a number of non-disease conditions can also cause high levels

of the biomarker. Individuals without the disease have biomarker levels that are normally

distributed with mean 1.6 ng/mL (nanograms per milliliter of blood), and standard deviation

0.50 ng/mL. Individuals with the disease have biomarker levels that are normally

distributed with mean 5 ng/mL and standard deviation 1.2 ng/mL. Values of 2.5 ng/mL

and higher constitute a positive test result. In a population where 6% of individuals are thought to have the hypothetical disease,

calculate the probability that an individual who tests positive has the disease.

1. The concentration of particles in a suspension is 49 per mL. A 5 mL volume of the suspension is withdrawn.

What is the probability that the number of particles withdrawn will be between 235 and 265?

2. a sample of 100 steel wires the average breaking strength is 46 kN, with a standard deviation of 2 kN.

Find a 95% confidence interval for the mean breaking strength of this type of wire. Round the answers to three decimal places.

The 95% confidence interval is (_,_ ).

Find a 99% confidence interval for the mean breaking strength of this type of wire. Round the answers to three decimal places.

The 99% confidence interval is (_,_ ).

An engineer claims that the mean breaking strength is between 45.7 kN and 46.3 kN. With what level of confidence can this statement be made? Express the answer as a percent and round to two decimal places.

The level of confidence is _%.

Please answer the following questions and show all work and make sure I can read your writing please.

1) Ethan went on a 10 day fishing trip. The number of small mouth bass caught and released by Ethan each day was as follows.

Day 1 2 3 4 5 6 7 8 9 10

# of Fish 9 24 8 9 5 8 9 10 8 10

A. Find the mean, median, and mode

B. Find the range, variance, and sample standard deviation

2) A multiple-choice test consists of 20 questions. A student has to answer at least 9 questions correctly to pass the test. Use BINOMIAL DISTRIBUTION to find the probability that a student at random will pass the test?

A community is currently being served a single self-serve gas station with six pumps. A competitor is opening a new facility with 12 pumps across town. The table below shows the travel times in minutes from the four different areas in the community to the sites and the number of customers in each area.

(a) Using the Huff retail location model and if λ = 2, calculate the probability of a customer traveling from each area to each site.

(b) Estimate the proportion of the existing market lost to the new competitor.

Travel Times to Gas Stations (in minutes)

Problem 6

a) Zoey Enterprises manufactures solar engines for helicopters. Given the fuel savings available, new orders for 125 units have been made by customers requesting credit. The variable cost is $11,400 per unit, and the credit price is $13,000 each. Credit is extended for one period. The required return is 1.9 percent per period. If Zoey Enterprises extends credit, it expects that 30 percent of the customers will be repeat customers and place the same order every period forever, and the remaining customers will place one-time orders. Should credit be extended?

b) Now, assume that the probability of default is 15 percent. Should the orders be filled now? Assume the number of repeat customers is affected by the defaults. In other words, 30 percent of the customers who do not default are expected to be repeat customers.

1. Refer to the Century National Bank data. Is it reasonable that the distribution of checking account balances approximates a normal probability distribution? Determine the mean and the standard deviation for the sample of 60 customers. Compare the actual distribution with the theoretical distribution. Cite some specific examples and comment on your findings.

2. Divide the account balances into three groups, of about 20 each, with the smallest third of the balances in the first group, the middle third in the second group, and those with the largest balances in the third group. Next develop a table that shows the number in each of the categories of the account balances by branch. Does it appear that account balances are related to the branch? Cite some examples and comment on your findings

this has already been posted on your site but the work how you got these answers are not please help!!

Suppose that a factory that produces shampoo has a machine that fills containers with c mL to 724 mL of shampoo.The machine is calibrated to fill bottles with at least the labeled amount (700 mL) 80% of the time. (a) Find the value of c. (b) The company that sells the product is worried that they are losing a significant profit by selling too many bottles that are filled too much (significantly overfilled). Suppose that the company begins to lose money for any bottle that has 712 mL or more. Find the probability that at least one fourth of a batch of 100 bottles is significantly overfilled. (c) What is the expected value of the number of overfilled bottles? (d) Do you think the company should be worried about their profit margins? Explain using previous answers or other probabilities.