# Stats Library

## Statistics Assignment Library

1. ##### Solved: A survey of 120 female freshman showed that 18 did not wish to work after marriage. Find the 95% confidence interval
A survey of 120 female freshman showed that 18 did not wish to work after marriage. Find the 95% confidence interval of the true proportion of females who do not wish to work after marriage. Solution Let $X$ denote the...
2. ##### Solved (Free): Let $Y_1, Y2, \cdots, Y_n$ be independent random variables such that each $Y_i$ has a gamma distribution with parameters
Let $Y_1, Y2, \cdots, Y_n$ be independent random variables such that each $Y_i$ has a gamma distribution with parameters $\alpha_i$ and $\beta$. That is, the distributions of the $Y$'s might have different $\alpha$'s, but all have the same value for...
3. ##### Solved: The time between release from prison and the commission of another crime is uniformly distributed between 0 and 5 years for a high-risk group
The time between release from prison and the commission of another crime is uniformly distributed between 0 and 5 years for a high-risk group. Give the equation and graph the pdf for X, the time between release and the commission...
4. ##### Solved: The article “Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants”
The article "Modeling Sediment and Water Column Interactions for Hydrophobic Pollutants" (Water Research [1984]: 1169-1174) suggests the uniform distribution on the interval from 7.5 to 20 as a model for x = depth (in centimeters) of the bioturbation layer in...
5. ##### Solved: The hardness of a piece of ceramic is proportional to the firing time. Assume that a rating system has been devised to rate the hardness of a ceramic piece
The hardness of a piece of ceramic is proportional to the firing time. Assume that a rating system has been devised to rate the hardness of a ceramic piece and that this measure of hardness is a random variable that...
6. ##### Solved: Suppose that a class in elementary statistics was allocated 15 minutes to complete a quiz. It can be assumed that the time X it takes to complete
Suppose that a class in elementary statistics was allocated 15 minutes to complete a quiz. It can be assumed that the time X it takes to complete the quiz is uniformly distributed over the interval [0, 15]. Suppose a student...
7. ##### Solved (Free): The following data represents viscosity measurements from a batch chemical process. The data is assumed to be normally distributed
The following data represents viscosity measurements from a batch chemical process. The data is assumed to be normally distributed. The batches are checked for conformance to specification. Batches whose viscosity lies between 84 and 96 are acceptable. A random sample...
8. ##### Solved:The lifetime $X$ of a device is an exponential random variable with mean = $1/R$
The lifetime $X$ of a device is an exponential random variable with mean = $1/R$. Suppose that due to irregularities in the production process, the parameter $R$ is random and has a gamma distribution. (a) Find the joint pdf of...
9. ##### Solved: The useful life of an electrical component is exponentially distributed with a mean of 2,500 hours
The useful life of an electrical component is exponentially distributed with a mean of 2,500 hours. a. What is the probability the circuit will last more than 3,000 hours? b. What is the probability the circuit will last between 2,500...
10. ##### Solved (Free): A course has two quizzes of equal weight, a midterm examination that has twice the weight of a quiz
A course has two quizzes of equal weight, a midterm examination that has twice the weight of a quiz, and a final examination that has twice the weight of the midterm exam. If a student obtains 54% and 60% on...