STAT 2810

Exam 1

Name______

Date______Section______

Problem 1 ( points)

As most of you are probably aware, the Appalachian State University Mountaineers football team has posted two wins in the last two weeks of competition. Listed below is a bar chart representing the three rushing leaders for ASU and the number of yards each gained in the first two games of the season.

(a)Create a frequency table that includes entries for frequency, percentages and cumulative frequency.

(b)Create a pie chart for the frequencies shown in your table. Make sure to label the axes appropriately.

Problem 2 ( points)

I spent most of my day Saturday walking around the campus of Appalachian State University and it occurred to me that prior to entering Kidd Brewer Stadium, students tend to drink heavily. In light of this epiphany, it occurred to me to perform a little impromptu survey. I asked several students how many drinks that had per week. Listed below is a boxplot and basic descriptive statistics of the results of my survey.

Descriptive Statistics

Variable N Mean Median TrMean StDev SE Mean

number o 30 8.967 10.000 9.192 4.575 0.835

Variable Minimum Maximum Q1 Q3

number o 0.000 15.000 7.000 12.000

a)What is the number of drinks that breaks this data set into an upper half and a lower half? ______

b)What is the number of drinks that separates the data set into the top 75% and the lower 25%? ______

c)How many total students were included in my survey? ______

d)What is the general shape of the distribution? Explain what statistics you used to determine the shape.

e)Determine a “range of usualness” for this data set and describe what this range tells us about our sample.

Problem 3 ( points)

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

a. What is the probability that a randomly selected mother will have a pregnancy lasting longer than 308 days?

b. What is the probability that a randomly selected mother will have a pregnancy lasting shorter than 245 days?

c. What is the probability that a randomly selected mother will have a pregnancy lasting between 260 and 302 days?

d. Find the 95th percentile for the lengths of pregnancies.

Problem 4 ( Points)

Below is a table that represents a weather forecaster’s results from predicting the weather over the last year. Use this table to answer the questions below.

Actual Results

Rain / Sun / Total
Forecast Rain / 159 / 16
Forecast Sun / 18 / 172
Total

a)Create a marginal distribution from this contingency table in the empty spaces shown above.

b)What percent of the time was the forecast correct?

c)What percent of the time was the forecast correct when the weather was predicted to be sunny?

d)What percent of the time was the forecast wrong when the weather was predicted to be rainy?

Problem 5 ( points)

In the 2006 season Appalachian State played 11 regular season football games. Listed below are the total number of points ASU scored in each of those games.

2321 41 41 45 56 14 27 40 42 31

a)Find the mean of this data set.

b)Find the median for this data set.

c)Find the mode for this data set.

d)Given that the standard deviation for this data set is 12.44 and the data is normally distributed, find a range of values that contains 68% of the total points scored.

e)Also find a range of values that includes 99.7% of the total points scored.

Problem 6 ( points)

In the graph shown below, I have shown the average number of children calculated every three years from 1900 to the present.

a. Identify an overall trend for this data set, ignore the indices at the bottom of the graph. What is happening to the average number of children as time progresses? How do you know?

b. There appears to be a large decline in the number of children from 1927 to 1942, to what can you contribute this decline?