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Estadıstica y Probabilidad • Jorge Domınguez y Domınguez • Jorge Axel Domınguez Lopez Alfaomega

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Variables numericas 1

�� ! � �� " � # �!�

$%�� !� �� ! %�!� � !&��!�� ' Max − Min = 61.8 − 24.5 = 37.3 �� (!�� )�� !�� * � �#� $� �� !�� "� � +� �(!�� ,%�!�� ! %�!� � !&��!� ��!�� -�& 63− 23 = 40� - �� # �� .� )�� '

�� !�� +� )�� 235 = 0.034 $ �� " � # �! �� '

�� /�� " � # � �� " �� 0 14 1 �� 2� # �� !� �� 0 34 1� $ �� !�� " �!�� #� $�� ! � �� ,� �� .� �� "� ! � �� 3� $� ��'porcentaje(�� " � #) = (34 ) ∗ 0.133 + 0.25 + 0.299 + (34 ) ∗ 0.1166 = 0.735

+� 4�� !�� !�� %�!�� !�� &�� !�� !� �� !�� ,� +��.�

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�� $ �� !�� 'rango = max−min = 1723− 1269 = 454.

�� 5� �� 'rango = 1726− 1267 = 459.

$�� (!�� 2� �� ' 4599 = 51�

� �� !�� $�� $�� !�� ' � *�6 �� !�� 3�� 7�� !�� !�� ,!��


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- ��,� �� 8��! � � ��&�� !�� ,� �� !�� ## �� $� �&!��'frecuencia(X < 1500) = 0.726.

)� �� !�� ,!�� %�� !� �� 3+" �� !�� ## ��

Alfaomega Estadıstica y Probabilidad • Jorge Domınguez y Domınguez • Jorge Axel Domınguez Lopez

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�� $ �� rango = max − min = 19.7 − 0 = 19.7�

� ��!�� rango = 21 − 0 = 21. �� 3 �� + � +� 8�� %�!�!�� 36 �� ,�� $� � 8��!� �� 8�

�� $� ��!�� !�� ,!�� !�� ,� �� $ �� ## �� ' rango = max−min = 187− 148 = 39. $ �� + �� 'rango = 192− 144 = 39.

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��0�� !�� "#19�.:�":+ :�2:�:+:�9*#


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)� !�� n = 120, �� ,�� 5� �� ! ! � !�� !�� 2 �� # �� $ ��!�� , �� rango = 61 − 16 = 45, $ �� ' rango = max − min =

58.7− 18.7 = 40. $�� ,!�� 8�� !�� !��!�� ,� ��'

- �� !�� ;� �� ' 1

5 . $� � ��!�� +# ;�� $�� !�� 45 ��

�� +#� �� 0!�� +# ;��1= 0.013.

��!��!�� 0�� +# � + ;��19 (15 )∗2+(45 )∗16 = 13.8. -�& �� 0��+# � + ;��19 13.8

120 = 0.115. $� �� ,� �� ### ��

��0!�� .# ;��19(15 ) ∗ 16 + 13 + 4 + 2 + 1 + 23.2. )��

��0!�� .# ;��19 23.2120 = 0.193.


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$� �� *"� �� <��!� �� 186 ��

�� * �� <�� <�� 1

86 ∗ 18 = 6.7. � ��0!�� <�196.7+ 11+ 7+ 5 = 29.7. =� ��& �� 0!�� <�1= 29.7

80 = 0.0.371. =� !� �� ,�� 3� ��<� � ! ��

4�� ,�� (��!�� %�!��!�� 3#6 �� !�� 0!�� +*"# >�19 14 + 18 + 11 + 7 + 5 = 55. -�&�� 0!�� +*"# >�19 55

80 = 0.688. � ��!& �� ,� �� ?�� !��


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��0! � �� 8�� !��1= 0.275 + 0.225 + 0.125 + 0.05 + 0.025 = 0.7 $ 3#6 �� !� ! � �� 8�� !��

��0�� + � 8��1= 0.2 + 0.275 + 0.225 = 0.7

��0! � �� " 8�� !��1= 0.05 + 0.025 = 0.075 )� ��!�� !��


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$� �� !�� , �� 8 !�� !� �� !��

)��!��' �� . �� 114 = 0.071

��# �� ( 3

14 ) ∗ 2 = 0.425, �� 0.42945 = 0.095

$ ��0!�� # ��1∼= 0.022 + 0.044 + 0.0095 = 0.067. @� �� !�� !��

)� � �� "#� �� 1114 �� "� � �� !�� 3

14 �� 3

14 ∗ 9 + 1.929 � �� 1.92945 = 0.043.

$ ��0!�� "# ��1∼= 0.043 + 0.088 + 0.066 + 0.022 = 0.22. �� !�� !�� ! � ��

A��!�� 0�� # � �"# ��1∼= 0.034+ 0.2444+ 0.2666+ 0.157 = 0.703. =��#�#�. �� 8 �� #� � #�� 3 �� "#� �� %�!�!�� 3#6 �� !�� !�� # ��


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$ �� ! � �� "# !�� (!�� !�� "#�A�� 0!�� "#1= 2

5 ∗ 5 + 2 = 4 � �� # � "# ��'A�� 0�� # � "#1= 2

5 ∗ 16 + 24 + 14 + 12 + 11 + 8 + 3 ∼== 79, �A�� 0!�� #1= 8 + 3

5 ∗ 16 ∼== 10


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