1 (a) How many samples are possible consisting of 5 bolts from a panel with 9 bolts? (Generally, the bolts are picked for a sample with repetition of bolts not allowed. Also, the order in which the bolts are picked does not matter).

(b) Now, assume a panel with 9 bolts contains 2 bad bolts. How many samples of 5 of the bolts contain only good bolts? (Consider a bolt to be good if it is not bad).

(c) A turnpike authority's quality control procedure consists of accepting a panel if all of the 5 inspected bolts from a panel with 9 bolts are good. Find the probability that such a panel containing 2 bad bolts is accepted. (In this question, please report your answer as a decimal accurate to three significant figures, such as .729, and not as a percentage, such as 72.9%).

(d) A turnpike authority's quality control procedure consists of rejecting a panel if one or more of the 5 inspected bolts from a panel with 9 bolts is bad. Find the probability that such a panel containing 2 bad bolts is rejected. (In this question, please report your answer as a decimal accurate to three significant figures, such as 0.729, and not as a percentage, such as 72.9%).

(e) If the turnpike authority uses a quality control procedure that has a 15% probability of accepting a panel with 2 bad bolts to inspect 300 panels, with 2 bad bolts in each panel, what is the expected (or mean) number of panels that will be accepted?

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 12 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.28 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is known

normal distribution of weights

uniform distribution of weights

n is large

σ is unknown

(c) Give a brief interpretation of your results in the context of this problem.

There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.    

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.

(d) Find the sample size necessary for an 80% confidence level with a maximal error of estimate E = 0.06 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
___________ hummingbirds

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 17 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.22 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is unknownσ is knownn is largeuniform distribution of weightsnormal distribution of weights

(c) Interpret your results in the context of this problem.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.    There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.14 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
hummingbirds

Problem 1

Suppose that we check for clarity in 50 locations in Lake Tahoe and discover that the average depth of clarity of the lake is 14 feet. Suppose that we know that the standard deviation for the entire lake's depth is 2 feet. What is the confidence interval for clarity of the lake with a 99% confidence level?   

Problem 2 Consider the following exercise: Suppose that a student is taking a multiple-choice exam in which each question has four choices. Assuming that she has no knowledge of the correct answer to any of the questions, she has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question.                                                                                                                  

1. If there are five multiple-choice questions on the exam, what is the probability that she will get five questions correct?

2. What is the probability that she will get no more than two questions correct?

      (3) Problem 3    The average number of vehicle arrivals at an intersection is five per minute. Find the probability that thirteen vehicles arrive in 3 minutes.

       ( 4) Problem 4 Researchers have conducted a survey of 1600 coffee drinkers asking how much coffee they drink in order to confirm previous studies. Previous studies have indicated that 72% of Americans drink coffee. The results of previous studies      

                                    Are provided in the survey below.

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 10 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.38 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

normal distribution of weightsn is largeσ is unknownσ is knownuniform distribution of weights

(c) Interpret your results in the context of this problem.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.    There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.13 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
hummingbirds

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 13 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.36 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

n is largeuniform distribution of weightsσ is unknownnormal distribution of weightsσ is known

(c) Interpret your results in the context of this problem.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.    There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.06 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
hummingbirds

Consider the following excerpts from a New York Times article:
Despite its early promise … Restoration has had trouble becoming a mass-market
player … What went wrong? High on its own buzz, the company expanded at breakneck
speed, more than doubling the number of stores, to 94, in the year and a half after the
stock offering … Company managers agree, for example, that Restoration’s original
inventory system, which called for all furniture to be kept at stores instead of a central
warehouse, was a disaster.
Let’s look at one Restoration Hardware product, a leather chair. Average weekly sales
of this chair in each store is normally distributed with mean 1.25 units and standard
deviation 0.5 units. The replenishment lead time is 12 weeks. There is information
system in place.
 If each store holds its own inventory, then what is the company’s average
inventory if the company policy is to target a 99.25 percent in-stock probability?
 Suppose Restoration Hardware builds a central warehouse to serve the 94
stores. The lead time from the supplier to the central warehouse is 12 weeks.
The lead time from the central warehouse to each store is one week. Suppose
the warehouse operates with a 99 percent in-stock probability, but the stores
maintain a 99.25 percent in-stock probability. If only inventory at the retail
stores is considered, what is Restoration’s average inventory?

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 20 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.22 gram. (a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.) (b) What conditions are necessary for your calculations? (Select all that apply.) -n is large -σ is known -σ is unknown -normal distribution of weights -uniform distribution of weights (c) Interpret your results in the context of this problem. -The probability to the true average weight of Allen's hummingbirds is equal to the sample mean. -There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region. -There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region. -The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20. -The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80. (d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.15 for the mean weights of the hummingbirds. (Round up to the nearest whole number.) ______ hummingbirds

An engineering firm with a good track record is known to have a 40% success rate in
getting state-government construction contracts. In a recent year, the firm submitted bids
on eight construction projects to be funded by the state-government. The bids for
different projects are assessed independently of each other.
i) CHOOSE which of these probability distributions is most appropriate to describe a random variable X defined as "the number of approved state-government construction contracts bid by the engineering firm in the recent year". *
X~Poisson(8)
X~Po(3.2)
X~Binomial(8,0.4)
X~Negative Binomial(8,0.4)
X~Geometric(0.4)
ii) Using the random variable X in question 1(i), which of the following mathematical expressions indicates: the probability that the engineering firm will not get any state-government construction contracts that they have bid in the recent year? *
P(X=8)
P(X > 1)
1 - P(X=0)
P(X is at most 0)
iii) Hence, which of the following answers is correct for the probability that the firm will not get any state-government construction contracts that they have bid in the recent year? *
0.0168
0.0408
0.6866
0.3134
0.9832
Y~Hypergeometric(8,2,5)
Y~Negative Binomial(2, 0.0408)
Y~Geometric(0.6)
Y~Binomial(8, 0.6)
Y~Negative Binomial(2, 0.0168)
Y~Negative Binomial(2, 0.6)

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 17 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.40 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is unknownn is large

σ is known normal

distribution of weights

uniform distribution of weights

(c) Interpret your results in the context of this problem.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.    The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.16 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
hummingbirds