# Recent questions in Statistics and Probability

Scatterplots

Scatterplots

Scatterplots

### How can you use a scatterplot to describe the relationship between two data sets?

High school statistics

### One bushel of apples from a dwarf apple tree is equal to 42 pounds. Write an expression to find the number of pounds of apples in any number of bushels. If one tree can produce 6 bushels, how many pounds of apples will an orchard of 100 trees produce?

Normal distributions

Two-way tables

### The _______ relative frequencies are the sums of each row and column in a two-way table. (joint, marginal, or conditional)

Normal distributions

Probability

### If there is a 25% chance that it will rain on any given day in Seattle, find the probability that it will rain for three consecutive days.

Normal distributions

Two-way tables

Two-way tables

Scatterplots

Scatterplots

### Use a scatterplot and the linear correlation coefficient r to determine whether there is a correlation between the two variables. x y 1 3 0 1 15 5 2 6 3 8

Normal distributions

### Refer to the Journal of Applied Psychology (Jan. 2011) study of the determinants of task performance. In addition to $$x_{1} =$$ conscientiousness score and $$x_{2} = \{1 \text{if highly complex job, 0 if not}\}$$, the researchers also used $$x_{3} =$$ emotional stability score, $$x_{4} =$$ organizational citizenship behavior score, and $$x_{5} =$$ counterproductive work behavior score to model y = task performance score. One of their concerns is the level of multicollinearity in the data. A matrix of correlations for all possible pairs of independent variables follows. Based on this information, do you detect a moderate or high level of multicollinearity? If so, what are your recommendations? $$x_{1}\ x_{2}\ x_{3}\ x_{4}$$ Conscientiousness $$(x_{1})$$ Job Complexity $$(x_{2}).\ 13$$ Emotional Stability $$(x_{3}).\ 62.\ 14$$ Organizational Citizenship $$(x_{4}).\ 24.\ 03.\ 24$$ Counterproductive Work $$(x_{5})-\ .23-\ .23-\ .02-\ .62$$

Normal distributions

### Maurice and Lester are twins who have just graduated from college. They have both been offered jobs where their take-home pay would be $2500 per month. Their parents have given Maurice and Lester two options for a graduation gift. Option 1: If they choose to pursue a graduate degree, their parents will give each of them a gift of$35,000. However, they must pay for their tuition and living expenses out of the gift. Option 2: If they choose to go directly into the workforce, their parents will give each of them a gift of $5000. Maurice decides to go to graduate school for 2 years. He locks in a tuition rate by paying$11,500 for the 2 years in advance, and he figures that his monthly expenses will be $1000. Lester decides to go straight into the workforce. Lester finds that after paying his rent, utilities, and other living expenses, he will be able to save$200 per month. Their parents deposit the appropriate amount of money in a money market account for each twin. The money market accounts are currently paying a nominal interest rate of 3 percent, compounded monthly. Lester works during the time that Maurice attends graduate school. Each month, Lester saves $200 and deposits this amount into the$5000 money market account that his parents set up for him when he graduated. If Lester's initial balance is $$u_{0}=5000,u_n$$ is the current month's balance, and $$u_{n−1}$$ is last month's balance, write an expression for un in terms of $$u_{n−1}$$.

Normal distributions

Two-way tables

Two-way tables

Scatterplots