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DPS 51280 FMW01: Business Mathematics and Statistics
STATISTICS Chapter 6 and 13: In- Exercise Activity 9. Received: _____ (out of 20)
- About what percent of x values from a normal distribution lie within one standard deviation (left and right) of the mean of that
distribution?
68% of x values lie between -1σ and +1σ of the mean
- The heights men fellow normal distribution with mean of 160 cm and standard deviation of 11 cm. what is the approximate % of men
between 137.5cm and 182.5 cm?
z =
௫ – ఓ
σ
ଵଷ.ହ - ଵ
11
ଵ଼ଶ .ହ - ଵ
11
About 95% of x values lie between - 2σ and +2σ of the mean
- Suppose X ~ N(–3, 1). Between what x values does 95.45% of the data lie? The range of x values is centered at the mean of the
distribution(i.e., –3).
z =
௫ – ఓ
σ
௫ – (-ଷ)
1
௫ ା ଷ
1
-2 = x + 3 X = -2 -3 X = -
௫ – (-ଷ)
1
௫ ା ଷ
1
+2 = x + 3 X = 2 -3 X = -
About 95% of x values lie between - 5σ and -1σ of the mean
- The following data represents the number of hours 12 different students watched television during the weekend and the scores of each
student who took a test the following Monday.
a.) Display the scatter plot.
b.) Calculate the correlation coefficient r.
Hours, x 0 1 2 3 3 5 5 5 6 7 7 10
Test score, y 96 85 82 74 95 68 76 84 58 65 75 50
b.)
∑௫௬ି (∑௫)(∑௬)
ඥ∑௫
మ
ି
( ∑௫
)
మ
ඥ∑௬
మ
ି
( ∑௬
)
మ
ଵଶ(ଷଶସ)ି (ହସ)(ଽ଼ )
ඥଵଶ(ଷଷଶ)ିହସ
మ
ඥଵଶ(଼ଷ )ି
( ଽ଼
)
మ
Negative correlation, as the number of hours spent in TV increases, the test scores tends to decrease
5. The percentage of smokers among the various age groups in UK is given in Table below:
a. Complete the table.
Age Mid-interval age Men Women
b. Plot a scatter diagram of men and women that smoke separately against age. Describe the trend and
calculate the correlation coefficient, r
MEN
0
10
20
30
40
50
60
70
0 5 10 15 20 25 30 35 40
Mid-Interval Age
Number of Smokers - Men
WOMEN
Mid-interval
age
Women xy x2 y
2
0
10
20
30
40
50
60
70
0 5 10 15 20 25 30 35
Mid-Interval Age
Number of Smokers - Women
ଶ
ଶ
ଶ
ଶ
(ହଵଽ.ହ)ି (ଶଷ)(ଵସ)
ඥ(ଵହହହ)ିଶଷ
మ
ඥ(ଷଵସ)ି (ଵସ)
మ
Negative correlation, when the age increases, the number of women that smoke tends to decrease
