Question

2021-06-05

asked 2021-05-01

Which distribution (standard normal or Student's t) did you use? Why? Do you need information about the soil water content distributions?

asked 2021-05-18

Solve by using the strategy Work Backward. A beetle needs to climb out of a crater that is 800 cm deep. It advances 120 cm each day, but is slips back 90 cm while resting each night. How many days will it take before this beetle successfully climbs out of the crater?

asked 2021-06-15

In government data, a house-hold consists of all occupants of a dwelling unit, while a family consists of 2 or more persons who live together and are related by blood or marriage. So all families form households, but some households are not families. Here are the distributions of household size and family size in the United States.

\(\text{Number of people}\\ \begin{array}{|l|c|c|c|c|c|c|c|} \hline & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \begin{array}{l} \text { Household } \\ \text { probability } \end{array} & 0.25 & 0.32 & 0.17 & 0.15 & 0.07 & 0.03 & 0.01 \\ \hline \begin{array}{l} \text { Family } \\ \text { probability } \end{array} & 0 & 0.42 & 0.23 & 0.21 & 0.09 & 0.03 & 0.02 \\ \hline \end{array}\)

Let H = the number of people in a randomly selected U.S. household and F = the number of people in a randomly chosen U.S. family. The standard deviations of the 2 random variables are \(\sigma H=1.421\) and \(\sigma F=1.249.\) Explain why this difference makes sense.

asked 2020-12-25

1. It specifies the specific shape of the curve which approximates certain sampling distributions.

2. It’s name is often abbreviated by the three capital letters CLT

3. The word Central within its name, is meant to signify its role of central importance in the mathematics of probability and statistics.

4. The accuracy of the approximation it provides, improves when the trial success proportion p is closer to \(50\%\).

5. It specifies the specific mean of the curve which approximates certain sampling distributions.

6. The accuracy of the approximation it provides, improves as the sample size n increases.

7. It specifies the specific standard deviation of the curve which approximates certain sampling distributions.

8. It is a special example of the particular type of theorems in mathematics, which are called limit theorems.