Consider the bivariate data:

x : 10 , 12 , 14 , 15 , 16

y : 8 , 7 , 5 , 4 , 1

Formulate the linear regression formula and estimate the value of y when x=5

The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.

a. Find the probability of a pregnancy lasting 307 days or longer. (ROUND TO 4 DECIMAL PLACES)

b. If the length of pregnancy is in the lowest 44​%, then the baby is premature. Find the length that separates premature babies from those who are not premature.

High-power experimental engines are being developed by the Stevens Motor Company for use in its new sports coupe. The engineers have calculated the maximum horsepower for the engine to be 580HP. Sixteen engines are randomly selected for horsepower testing. The sample has an average maximum HP of 610 with a standard deviation of 55HP. Assume the population is normally distributed.

Step 1 of 2 :  

Calculate a confidence interval for the average maximum HP for the experimental engine. Use a significance level of α=0.1. Round your answers to two decimal places.

A random sample of n₁ = 10 regions in New England gave the following violent crime rates (per million population).

x₁: New England Crime Rate

Another random sample of n₂ = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population).

x₂: Rocky Mountain Crime Rate

Find a 98% confidence interval for μ₁ − μ₂. (Round your answers to two decimal places.)

Lower Limit

Upper Limit

A sample of size =n47 has sample mean =x57.6 and sample standard deviation =s9.5. Part: 0 / 20 of 2 Parts Complete Part 1 of 2 Construct a 99.5% confidence interval for the population mean μ. Round the answers to one decimal place. A 99.5% confidence interval for the population mean μ is <<μ .

Let Y₁ < Y₂ < Y₃ < Y₄ < Y₅ be the order statistics of a random sample of size 5 from a continuous distribution with median m. What is P(Y₂ < m < Y₄)?

People tend to evaluate the quality of their lives relative to others around them. In a demonstration of this phenomenon, Frieswijk, Buunk, Steverink, and Slaets (2004) conducted fictitious interviews with frail elderly people. In the interview, each person was compared with others who were worse off. After the interviews, the elderly people reported more satisfaction with their own lives (the hypothetical data are reported below). The scores are measures on a life satisfaction scale for a sample of n = 9 elderly people who completed the interview are: 18, 23, 24, 22, 19, 27, 23, 26, 25.

Assume that the average score on this scale is m= 20. Are the data sufficient to conclude that the people in this sample are significantly more satisfied than others in the general population? Use a = .05.

The file Hotel Prices contains the prices in British pounds (about US$ 1.52 as of July 2013) of a room at two-star, three-star, and four-star hotels in cities around the world in 2013.

e. Compute the covariance between the average price at two-star and three-star hotels, between two-star and four-star hotels, and between three-star and four-star hotels.

f. Compute the coefficient of correlation between the average price at two-star and three-star hotels, between two-star and four-star hotels, and between three-star and four-star hotels.

g. Which do you think is more valuable in expressing the relation-ship between the average price of a room at two-star, three-star, and four-star hotels—the covariance or the coefficient of cor-relation? Explain.

h. Based on (f), what conclusions can you reach about the relationship between the average price of a room at two-star, three-star, and four-star hotels?

Elderly drivers. A polling agency interviews 754 American adults and finds that 467 think licensed drivers should be required to retake their road test once they reach 65 years of age. Round all answers to 4 decimal places.

1. Calculate the point estimate for the proportion of American adults that think licensed drivers should be required to retake their road test once they reach 65 years of age.  

2. Calculate the standard error for the point estimate you calculated in part 1.  

3. Calculate the margin of error for a 99% confidence interval for the proportion of American adults that think licensed drivers should be required to retake their road test once they reach 65 years of age.

4. What are the lower and upper limits for the 99% confidence interval? ( ,  )

5. Use the information from the polling agency to determine the sample size needed to construct a 99% confidence interval with a margin of error of no more than 5%. For consistency, use the reported sample proportion for the planning value of p* (rounded to 4 decimal places) and round your Z* value to 3 decimal places. Your answer should be an integer.

The average weight of vegan men standing between 5 foot 9 inches and 5 foot 11 inches is 145lbs.with a standard deviation of 5 lbs. What are the minimum and maximum weights rounded to pounds for vegan men (in this height range) in the middle 78.5%?
a.) (141 lbs., 149 lbs.) b.) (134 lbs.,156 lbs.) c.) (139 lbs., 151 lbs.) d.) (150 lbs., 170 lbs.) e.) None of these.

When a convicted felon leaves prison and is on parole it can be a daunting task to find employment. Fortunately there exist farmers markets which offer employment suitable to recently paroled felons. At the Hermosa Beach farmers market 7 of the 13 farmers market employees are recently paroled felons. If the police select at random 4 employees at the Hermosa Beach farmers market what is the probability 2 of them are recently paroled felons?
a.) 0.4406 b.) 0.3381 c.) 0.3147 d.) 0.5454 e.) None of these

A ski resort losses $70,000 per season when it doesn’t snow very much and makes $250,000 profit when it does snow a lot. The probability of it snowing a lot is 40%. The expectation for the profit is
a.) $58,000 b.) $292,000 c.) $72,000 d.) $42,000 e.) None of these

At Litchfield College of Nursing, 87% of incoming freshmen nursing students are female and 13% are male. Recent records indicate that 60% of the entering female students will graduate with a BSN degree, while 80% of the male students will obtain a BSN degree. If an incoming freshman nursing student is selected at random, find the following probabilities. (Enter your answers to three decimal places.)

(a) P(student will graduate | student is female)


(b) P(student will graduate and student is female)


(c) P(student will graduate | student is male)


(d) P(student will graduate and student is male)


(e) P(student will graduate). Note that those who will graduate are either males who will graduate or females who will graduate.


(f) The events described the phrases "will graduate and is female" and "will graduate, given female" seem to be describing the same students. Why are the probabilities P(will graduate and is female) and P(will graduate | female) different?

-The term given refers to the sample space of all students, while the term and refers to restricting the sample space to females only.

-The term and refers to the sample space of all students, while the term given refers to restricting the sample space to females only.     

-These probabilities are the same.This is by chance.

-These probabilities are typically the same.

An urn contains 10 red balls and 5 green balls. Balls are randomly selected, one at a time, with replacement, until a red one is obtained. What is the probability that exactly k draws are needed? What is the probability that at least k draws are needed? Define a random variable associated with this experiment. Determine its probability mass function and cumulative distribution function, sketch their graphs. Find the expectation, variance and standard deviation of X.