The heights of a given population are normally distributed - Leaving Cert Mathematics - Question 5 - 2021
Question 5
The heights of a given population are normally distributed. 95% of the population fall within the height range [147.9 cm ↔ 178.7 cm].
Using the empirical rule, find ... show full transcript
Worked Solution & Example Answer:The heights of a given population are normally distributed - Leaving Cert Mathematics - Question 5 - 2021
Step 1
Mean =
96%
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Answer
To find the mean height of the population, we can average the two given values:
extMean=2147.9+178.7=163.3 cm
Step 2
Standard Deviation =
99%
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Answer
The empirical rule states that approximately 95% of values lie within 2 standard deviations from the mean. Thus:
ext2standarddeviations=178.7−163.3=15.4 cm
This implies that:
σ=215.4=7.7 cm, where ( ext{\sigma}) is the standard deviation.
Step 3
Complete the scatter plot by adding in the data for the males
96%
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Answer
The male data extracted from the table is:
Gender
Height (cm)
Arm Span (cm)
14
M
147
15
M
134
16
M
177
17
M
172
18
M
160
19
M
165
20
M
175
These points should be plotted on the scatter plot.
Step 4
Tick (✓) the one which you think best represents the correlation coefficient between height and arm span for this data set.
98%
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Answer
The correlation coefficient should reflect a strong positive relationship. Hence, I would tick the box for
0-6 as it indicates a high positive correlation.
Step 5
Explain what this correlation coefficient tells us about the relationship between height and arm span for this data set.
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A correlation coefficient close to 1 (in this case, 0.6) suggests a strong positive linear relationship between height and arm span. This means that, generally, as height increases, the arm span also tends to increase. Taller teenagers are likely to have a longer arm span, indicating a proportional increase in these two physical characteristics.
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