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STAT-1770-B1-Intro. to Probability & Stat.

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The percent of fat calories that a person in America consumes each day is

normally distributed with a mean of about 36 and a standard deviation of

10. Suppose that one individual is randomly chosen. Let X = percent of

fat calories.

(a) X ∼ -(-,-) ? 

(b) Find the probability that the percent of fat calories a person

consumes is more than 40. Graph the situation. Shade in the area to

be determined.

(c) Find the maximum number for the lower quarter of percent of fat

calories. Sketch the graph and write the probability statement

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The following are advertised sale prices of color televisions at Anderson’s

Size (inches) Sale Price ($)
9 147
20 197
27 297
31 447
35 1177
40 2177
60 2497

(a) Decide which variable should be the independent variable and which

should be the dependent variable.

(b) Draw a scatter plot of the data.

(c) Does it appear from inspection that there is a relationship between

the variables? Why or why not?

(d) Calculate the least-squares line. Put the equation in the form of:

y^ = a + bx

(e) Find the correlation coefficient. Is it significant?

(f) Find the estimated sale price for a 32 inch television. Find the cost

for a 50 inch television.

(g) Does it appear that a line is the best way to fit the data? Why or

why not?

heart Are there any outliers in the data?

(i) What is the slope of the least-squares (best-fit) line? Interpret the

slope

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The percent of female wage and salary workers who are paid hourly rates is given in Table below for the years 1979 to 1992.

Year Percent of workers paid hourly rates
1979 61.2
1980 60.7
1981 61.3
1982 61.3
1983 61.8
1984 61.7
1985 61.8
1986 62.0
1987 62.7
1990 62.8
1992 62.9

(a) Using "year" as the independent variable and "percent" as the dependent variable, draw a scatter plot of the data.

(b) Does it appear from inspection that there is a relationship between

the variables? Why or why not?

(c) Calculate the least-squares line. Put the equation in the form of y = a + bx

(d) Find the correlation coefficient. Is it significant?

(e) Find the estimated percents for 1991 and 1988.

(f) Based on the data, is there a linear relationship between the year and

the percent of female wage and salary earners who are paid hourly rates?

(g) Are there any outliers in the data?

heart What is the estimated percent for the year 2050? Does the

least-squares line give an accurate estimate for that year?

(i) What is the slope of the least-squares (best-fit) line? Interpret the slope.

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