A soft-drink bottling company maintains records of the number of unacceptable bottles obtained from its two filling and capping machines. A trial inspection of a production run of 1000 bottles showed that 430 came from Machine I and 570 from Machine II. Ten bottles from Machine I and 25 from Machine II were nonconforming.

(a) Use the above information to estimate the probabilities in the contingency table:

(b) What proportion of the total output is nonconforming?

(c) If a randomly-chosen bottle is found to be nonconforming, what is the probability that it was produced on Machine II?

(d) Which machine seems to be better? Calculate relevant probabilities and discuss.     

Health Niagara is working on its 2021 budget. According to data from the last fiscal year, 30% of people between 60-70 years old will have at least one visit to a health provider. This proportion will be 5% for people between 10-20 years old, and it will be 15% for kids between 5-10 years old. If we randomly select 75 of people in the age range of 60-70, then answer the following questions: Question 4: What is the expected number of those who will visit a health provider? a) 52.5 b) 30 c) 15.75 d) 22.5

5.What is the probability that at least 15 people will visit a health provider? a) 0.96 b) 0.98 c) 0.04 d) 0.02

A company in the food industry stores a large number of canned goods in a central warehouse. Last year, 3% of the canned goods had damage (for example, ugly worms or dents in the can), and the warehouse manager suspects it could be even worse this year.

To investigate this, we randomly selected 260 of the preserves and of these, 13 have
damage.
(a) Conduct hypothesis testing to test if the warehouse manager's suspicions can be considered where
Acknowledged.
(b) Formulate an interpretation of the P-value for the test in the (a) assignment. (The P value is
probability of ...)
(c) If we did the investigation, how could we do it to get higher?
strength of the test in the (a) assignment? Justify the answer.
(d) Describe what a Type I error and a Type II error would mean in this context.

A researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The table shows the results for the number of bacteria per cubic foot for both types of rooms.

Full data set   

10. Continuing with the same population in Question 7, let us consider the case where we picked a sample of size 14. (Do not worry

about the fact that it is stupid to have a sample of size 14 when the population has only 4 people in it.) What is the standard error

(deviation) of the sampling distribution of the mean?

11. You need to clean out a fish tank, so you get a small bowl to take out all the fish one at a time. You have 20 betta fish and 5 gold

fish. Assuming that each fish in the tank has an equal likelihood of being taken out, is the probability of getting a certain number of betta

fish in the first four draws a binomial distribution? Please explain.

The number of patients needing admission each day to a hospital intensive care unit (ICU) has a Poisson distribution with a mean of 5.3. (a) Why might it be reasonable to expect that daily numbers of patients would have a Poisson distribution rather than any other distribution? (b) Assuming that patients only stay in the ICU for one day, what is the probability that an 8-bedded ICU will have to turn patients away on any particular day? (c) How many beds would the ICU require to ensure that patients, on average , were only turned away one day per year? (d) What are the practical implications of your analyses if a hospital wishes to achieve a high level of usage for its ICU beds?

The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2979 and standard deviation 593. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( 2979 Correct, 593 Correct) b. Find the probability that the customer consumes less than 2587 calories. c. What proportion of the customers consume over 3353 calories? d. The Piggy award will given out to the 1% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award? calories. (Round to the nearest calorie)

A company in the food industry stores a large number of canned goods in a central warehouse. Last year, 3% of the canned goods had damage (for example, ugly worms or dents in the can), and the warehouse manager suspects it could be even worse this year.

To investigate this, we randomly selected 260 of the preserves and of these, 13 have
damage.
(a) Conduct hypothesis testing to test if the warehouse manager's suspicions can be considered where
Acknowledged.
(b) Formulate an interpretation of the P-value for the test in the (a) assignment. (The P value is
probability of ...)
(c) If we did the investigation, how could we do it to get higher?
strength of the test in the (a) assignment? Justify the answer.
(d) Describe what a Type I error and a Type II error would mean in this context.

1. A university has 10,000 students of which 45% are male and 55% are female. If a class of 30 students is chosen at random from the university population, find the mean and variance of the number of male students. Group of answer choices Mean = 16.5, Variance = 2.7 Mean = 13.5, Variance = 2.7 Mean = 16.5, Variance = 7.4 Mean = 13.5, Variance = 7.4

2. At a particular hospital, 40% of staff are nurse assistants. If 12 staff members are randomly selected, what is the probability that exactly 4 are nurse assistants?

3. Let X be a binomial distribution with n = 20 and p = .4 then the variance is

4.

Find the mean of the distribution shown below.

#2). Under-coverage is a problem that occurs in surveys when some groups in the population are underrepresented in the sampling frame used to select the sample. We can check for under-coverage by comparing the sample with known facts about the population.

a. Suppose we take a SRS of n=500 people from a population that is 25% Hispanic. How many Hispanics are expected in a given sample? [2 points]

b. What is the standard deviation for the number of Hispanics in a sample? [2 points]

c. Can the normal approximation to the binomial be used to help make probabilistic statements about samples from this population? [2 points]

d. Determine the probability that a sample contains 100 or fewer Hispanics under the stated conditions.[4 points]