The normal distribution curve which models, distributions of data in a wide range of applications, is given by the function 
where 
and ? and ? are constants called the standard deviation and the mean, respectively. Its graph is shown in the figure.
?
?
In a survey, consumers were asked to rate a new toothpaste on a scale of 1-10. The resulting data are modeled by a normal distribution with 
and 
. The percentage of consumers who gave the toothpaste a score between a and b on the section is given by 
?
Use a Riemann sum with n = 10 to estimate the percentage of customers who rated the toothpaste 5 or higher. (Use the range 4.5 to 10.5.) Round your answer to the nearest whole number.
?
A. 45%
B. 46%
C. 47%
D. 48%
E. 49%
Answer: C
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Use the guidelines to evaluate the study. Discuss flaws that you see in the study. A researcher is interested in why Americans have such a high divorce rate. She randomly selects 100 American married couples and 100 Japanese married couples. She invites each couple to come into her office and interviews each couple, asking them about their satisfaction with their marriage. The researcher also notes that a high percentage of the American women had full time jobs outside the home, whereas a high percentage of the Japanese women did not have full time jobs. The researcher concluded that marriages in which the woman has a full time job have a lower rate of success.
What will be an ideal response?
The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an equation for the stretched or compressed graph.y = 1 + 
compressed horizontally by a factor of 9
A. y = 1 + 
B. y = 
+ 
C. y = 1 + 
D. y = 9 + 
Solve the problem.Shown is the image of a figure under the two successive translations that take P to P' and then P' to P''. Find the original figure. Note again, the given figure is the image after translation. Hint: First find the final image of a point if it were translated by both translations. Then what happens in the reverse process?
A. 
B. 
C. 
D. 
Solve.The number of centimeters, d, that a spring is compressed from its natural, uncompressed position is given by the formula 
where W is the number of joules of work done to move the spring and k is the spring constant. Solve this equation for W. Use the result to determine the work needed to move a spring 9 centimeters if it has a spring constant of 0.4.
A. W = 
B. W = 
C. W = 2d2k
D. W = 