8.6. Refer to Exercise 8.5. Compute 10-year increments of the population growth x1 = 5.3−3.9, x2 = 7.2 − 5.3, etc. (a) Compute sample mean, median, and variance of 10-year increments. Discuss how the U.S. population changes during a decade. (b) Construct a time plot of 10-year increments and discuss the observed pattern.

8.6. Refer to Exercise 8.5. Compute 10-year increments of the population growth x1 = 5.3−3.9,
x2 = 7.2 − 5.3, etc.
(a) Compute sample mean, median, and variance of 10-year increments. Discuss how the
U.S. population changes during a decade.
(b) Construct a time plot of 10-year increments and discuss the observed pattern.

a)  Mean = 13.88

Median = 13

Variance= 87.6035

Note: The rate of change is increasing after each decade. 

b) 

 

Construct a time plot for the U.S. population. What kind of trend do you see? What information can be extracted from this plot?

The following data set shows population of the United States (in million) since 1790,
Year:  1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900
Population:  3.9 5.3 7.2 9.6 12.9 17.1 23.2 31.4 38.6 50.2 63.0 76.2
Year 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
Population 92.2 106.0 123.2 132.2 151.3 179.3 203.3 226.5 248.7 281.4 308.7
Construct a time plot for the U.S. population. What kind of trend do you see? What information
can be extracted from this plot?

• ·         The year and population seems positively co-related because population increases when the year increases.

• ·         From this plot we can figure out the growth of total population.

8.9. The following data set represents the number of new computer accounts registered during ten consecutive days. 43, 37, 50, 51, 58, 105, 52, 45, 45, 10. (a) Compute the mean, median, quartiles, and standard deviation.

8.9. The following data set represents the number of new computer accounts registered during
ten consecutive days.
43, 37, 50, 51, 58, 105, 52, 45, 45, 10.
(a) Compute the mean, median, quartiles, and standard deviation.

8.8. Consider three data sets. (1) 19, 24, 12, 19, 18, 24, 8, 5, 9, 20, 13, 11, 1, 12, 11, 10, 22, 21, 7, 16, 15, 15, 26, 16, 1, 13, 21, 21, 20, 19 (2) 17, 24, 21, 22, 26, 22, 19, 21, 23, 11, 19, 14, 23, 25, 26, 15, 17, 26, 21, 18, 19, 21, 24, 18, 16, 20, 21, 20, 23, 33 (3) 56, 52, 13, 34, 33, 18, 44, 41, 48, 75, 24, 19, 35, 27, 46, 62, 71, 24, 66, 94, 40, 18, 15, 39, 53, 23, 41, 78, 15, 35 (a) For each data set, draw a histogram and determine whether the distribution is rightskewed, left-skewed, or symmetric.

8.8. Consider three data sets.
(1) 19, 24, 12, 19, 18, 24, 8, 5, 9, 20, 13, 11, 1, 12, 11, 10, 22, 21, 7, 16, 15, 15, 26, 16, 1,
13, 21, 21, 20, 19
(2) 17, 24, 21, 22, 26, 22, 19, 21, 23, 11, 19, 14, 23, 25, 26, 15, 17, 26, 21, 18, 19, 21, 24,
18, 16, 20, 21, 20, 23, 33
(3) 56, 52, 13, 34, 33, 18, 44, 41, 48, 75, 24, 19, 35, 27, 46, 62, 71, 24, 66, 94, 40, 18, 15,
39, 53, 23, 41, 78, 15, 35
(a) For each data set, draw a histogram and determine whether the distribution is right skewed,
left-skewed, or symmetric.
 (b) Compute sample means and sample medians. Do they support your findings about
skewness and symmetry? How?

4.23. The lifetime of a certain electronic component is a random variable with the expectation of 5000 hours and a standard deviation of 100 hours. What is the probability that the average lifetime of 400 components is less than 5012 hours?

4.23. The lifetime of a certain electronic component is a random variable with the expectation of
5000 hours and a standard deviation of 100 hours. What is the probability that the average
lifetime of 400 components is less than 5012 hours?

4.21. The average height of professional basketball players is around 6 feet 7 inches, and the standard deviation is 3.89 inches. Assuming Normal distribution of heights within this group, (a) What percent of professional basketball players are taller than 7 feet? (b) If your favorite player is within the tallest 20% of all players, what can his height be?

4.21. The average height of professional basketball players is around 6 feet 7 inches, and the
standard deviation is 3.89 inches. Assuming Normal distribution of heights within this
group,
(a) What percent of professional basketball players are taller than 7 feet?
(b) If your favorite player is within the tallest 20% of all players, what can his height be?

4.11. Consider a satellite whose work is based on a certain block A. This block has an independent backup B. The satellite performs its task until both A and B fail. The lifetimes of A and B are exponentially distributed with the mean lifetime of 10 years. (a) What is the probability that the satellite will work for more than 10 years? (b) Compute the expected lifetime of the satellite.

4.11. Consider a satellite whose work is based on a certain block A. This block has an independent
backup B. The satellite performs its task until both A and B fail. The lifetimes of A and B
are exponentially distributed with the mean lifetime of 10 years.
(a) What is the probability that the satellite will work for more than 10 years?
(b) Compute the expected lifetime of the satellite.