Fire damage in the United States amounts to billions of dollars, much of it insured. The time taken to arrive at the fire is critical. This raises the question, Should insurance companies lower premiums if the home to be insured is close to a fire station? To help make a decision, a study was undertaken wherein a number of fires were investigated. The distance to the nearest fire station (in miles) and the percentage of fire damage were recorded. Determine the least squares line and interpret the coefficients

The term regression was originally used in 1885 by Sir Francis Galton in his analysis of the relationship between the heights of children and parents. He formulated the “law of universal regression,” which specifies that “each peculiarity in a man is shared by his kinsmen, but on average in a less degree.” (Evidently, people spoke this way in 1885.) In 1903, two statisticians, K. Pearson and A. Lee, took a random sample of 1,078 father–son pairs to examine Galton’s law (“On the Laws of Inheritance in Man, I. Inheritance of Physical Characteristics,” Biometrika2:457–462). Their sample regression line was Son's height $=33.73+.516 \times$ Father's height. What does the regression line tell you about the heights of sons of tall fathers?

The term regression was originally used in 1885 by Sir Francis Galton in his analysis of the relationship between the heights of children and parents. He formulated the “law of universal regression,” which specifies that “each peculiarity in a man is shared by his kinsmen, but on average in a less degree.” (Evidently, people spoke this way in 1885.) In 1903, two statisticians, K. Pearson and A. Lee, took a random sample of 1,078 father–son pairs to examine Galton’s law (“On the Laws of Inheritance in Man, I. Inheritance of Physical Characteristics,” Biometrika2:457–462). Their sample regression line was Son's height $=33.73+.516 \times$ Father's height. What does the regression line tell you about the heights of sons of short fathers?

The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 12,200. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 820 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last. How many pages should the manufacturer advertise for each cartridge if it wants to be correct 99 percent of the time?

The Tesla Model S 85D is an electric car that the manufacturer claims can travel 270 miles on a single charge. However, the actual distance depends on a number of factors including speed and whether the car is driven in the city or on highways. Suppose that the distance is a normally distributed random variable with a mean of 200 miles and a standard deviation of 20 miles. An owner of this model intends to travel to a nearby city and return on the same charge. If the total distance is 210 miles, what is the probability that car makes it without running out of power?

The following density function describes the random variable X .Graph the density function.

$$f(x)=\left\{\begin{array}{cl}\frac{x}{25} & 0<x<5 \\ \frac{10-x}{25} & 5<x<10\end{array}\right.$$

A uniformly distributed random variable has minimum and maximum values of 20 and 60, respectively. Determine $P(35<X<45)$.

Hits on a personal website occur quite infrequently. They occur randomly and independently with an average of five per week. Determine the probability that the site gets 20 or more hits in 2 weeks.

Hits on a personal website occur quite infrequently. They occur randomly and independently with an average of five per week.. Find the probability that the site gets 10 or more hits in a week

According to a New York Times/CBS News poll conducted during June $24-28,2011,55 \%$ of the American adults polled said that owning a home is a very important part of the American Dream (The New York Times, June 30, 2011). Assume that all adult Americans in 2011 experienced this outcome. A recent survey of 1800 American adults found that 61% of them believe that having a home is an essential component of the American Dream. Make a hypothesis test to determine whether it is reasonable to claim that more than 55 percent of American adults have this viewpoint at the moment. Use the $p$-value and the critical-value techniques with a $2\%$ significance level.

Suppose $X$ is a binomial random variable with $n = 25$ and $p = .7$. Use Table 1 to find the following: $P(X ≤ 20)$

Suppose $X$ is a binomial random variable with $n = 25$ and $p = .7$. Use Table 1 to find the following: $P(X = 15)$

Suppose X is a binomial random variable with n = 25and p = .7. Use Table 1 to find the following: P(X = 18)

Suppose $X$ is a binomial random variable with $n = 25$ and $p = .7$. Use Table 1 to find the following: $P(X ≥ 16)$