1) What are all the values that a standard deviation s can possible take?
(a) 0 ≤ s
(b) -1 ≤ s ≤ 1
(c) 0 ≤ s ≤ 1
(d) s can be any number.
2) If a distribution of a set of data is skewed to the right, then
(a) the mean and the median are equal.
(b) the mean is greater than median.
(c) the mean is less than the median.
(d) we need to know more information such standard deviation to decide.
3) The scores of the USA adults on an IQ test are approximately Normal with mean 100 and standard deviation 15. An IVY university requires an IQ score of 130 or higher for admission. What percent of adults would not qualify for admission?
(a) 97.5%
(b) 2.5%
(c) 95%
(d) 5%
4) The points on a scatterplot lie very close to a straight line. The correlation between x and y is close to
(a) -1
(b) either -1 or 1, we can't say which. 1
(c) 1
(d) need more information
5) In a study exercise, a large group of male runners walk on a treadmill for 6 minutes. Their heart rates in beats per minute at the end vary from runner to runner according to the N(104, 12.5) distribution. The heart rates for male non-runners after the same exercise have the N(130, 17) distribution.
(a) What percent of the runners have heart rates above 135?
(b) What percent of the non-runners have heart rates above 135?
(c) How high must a runner heart rate to place in the top 10% of all runners?
6) Here are the exam scores of 25 randomly selected students from a Math 140B class.
50, 35, 41, 97, 76, 69, 94, 91, 23, 65, 56, 38, 48, 92, 79, 66, 94, 95, 90, 93, 11, 77, 92, 99, 25
Make a stemplot of these data and comment on the shape of the distribution of the data.
7) The most popular colors for cars and light trucks vary with region and over time. In North America white remains the top color choice, with silver the top choice in South America and white the top choice worldwide for second consecutive year. Here is the distribution of the top colors of vehicles sold in North America in 2014:
|
Color
|
Popularity
|
|
White
|
26%
|
|
Black
|
21%
|
|
Silver
|
18%
|
|
Red/Brown
|
15%
|
|
Other colors
|
|
Make a pie chart and a bar graph to display the distribution of color popularity. (Hint: first fill in the percent of the vehicles that are in other colors.)
8) Use Table A to find the proportion of observations from a standard Normal distribution that falls in each of the following regions. In each case, sketch a standard Normal curve and shade the area representing the region.
(a) z ≤ -2.14 (b) z ≥ 2.16 (c) - 2.11 < z < 1.16
9) The deadly Ebola virus is a threat to both people and gorillas in Central Africa. An outbreak in 2002 and 2003 killed 91 of 95 gorillas in seven home ranges in the Congo. To study the spread of the virus, measure "distance" by the number of home ranges separating a group of gorillas from the first group infected. Here are data on distance and time in number of days until deaths began in each later group:
|
Distance
|
1
|
3
|
4
|
4
|
5
|
6
|
|
Time
|
4
|
21
|
33
|
38
|
45
|
55
|
(a) Make a scatterplot. Which is the explanatory variable? What kind of pattern does your plot show?
(b) Find the correlation r between distance and time. (Show your work.)
(c) Find the regression equation. (Show your work.)
(d) What does the slope of the line say about the relationship between the distance and time until deaths began?
(e) What is the predicted time for a home 5.5 miles away?