Mathematics
Grade10
Easy

Question


Approximately ______ of data values in a normal distribution within 1 standard deviation of the mean.

  1. 68% 
  2. 69% 
  3. 70% 
  4. 100% 

The correct answer is: 68%


    68 percent sign comma space i s space t h e space c o r r e c t space c h o i c e

n o r m a l space d i s t r i b u t i o n space h a s space s o m e space i n t e r e s t i n g space p r o p e r t i e s colon
rightwards arrow space i t space h a s space a space b e l l space s h a p e comma
rightwards arrow space t h e space m e a n comma space m e d i a n space a n d space m o d e space a r e space e q u a l comma
rightwards arrow space 68 percent sign space o f space t h e space d a t a space f a l l s space w i t h i n space 1 space s tan d a r d space d e v i a t i o n.

    p r o p e r t i e s space o f space n o r m a l space d i s t r i b u t i o n colon

rightwards double arrow i t space i s space a space b e l l space s h a p e d space c u r v e
rightwards double arrow T h e space m e a n comma space m o d e space a n d space m e d i a n space a r e space a l l space e q u a l. space
rightwards double arrow i t space i s space s y m m e t r i c space a b o u t space t h e space m e a n comma space mu.
rightwards double arrow space T h e space t o t a l space a r e a space u n d e r space t h e space c u r v e space i s space 1.
rightwards double arrow 68 percent sign space o f space t h e space d a t a space f a l l s space w i t h i n space 1 space s tan d a r d space d e v i a t i o n.
rightwards double arrow space 99.7 percent sign space o f space d a t a space o b s e r v e d space f o l l o w i n g space a space n o r m a l space d i s t r i b u t i o n space l i e s space w i t h i n space 3 space s tan d a r d space d e v i a t i o n s space o f space t h e space m e a n.

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    p r o p e r t i e s space o f space n o r m a l space d i s t r i b u t i o n colon

rightwards double arrow i t space i s space a space b e l l space s h a p e d space c u r v e
rightwards double arrow T h e space m e a n comma space m o d e space a n d space m e d i a n space a r e space a l l space e q u a l. space
rightwards double arrow i t space i s space s y m m e t r i c space a b o u t space t h e space m e a n comma space mu.
rightwards double arrow space T h e space t o t a l space a r e a space u n d e r space t h e space c u r v e space i s space 1.
rightwards double arrow 68 percent sign space o f space t h e space d a t a space f a l l s space w i t h i n space 1 space s tan d a r d space d e v i a t i o n.
rightwards double arrow space 99.7 percent sign space o f space d a t a space o b s e r v e d space f o l l o w i n g space a space n o r m a l space d i s t r i b u t i o n space l i e s space w i t h i n space 3 space s tan d a r d space d e v i a t i o n s space o f space t h e space m e a n.

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    p r o p e r t i e s space o f space n o r m a l space d i s t r i b u t i o n colon

rightwards double arrow i t space i s space a space b e l l space s h a p e d space c u r v e
rightwards double arrow T h e space m e a n comma space m o d e space a n d space m e d i a n space a r e space a l l space e q u a l. space
rightwards double arrow i t space i s space s y m m e t r i c space a b o u t space t h e space m e a n comma space mu.
rightwards double arrow space T h e space t o t a l space a r e a space u n d e r space t h e space c u r v e space i s space 1.
rightwards double arrow 68 percent sign space o f space t h e space d a t a space f a l l s space w i t h i n space 1 space s tan d a r d space d e v i a t i o n.
rightwards double arrow space 99.7 percent sign space o f space d a t a space o b s e r v e d space f o l l o w i n g space a space n o r m a l space d i s t r i b u t i o n space l i e s space w i t h i n space 3 space s tan d a r d space d e v i a t i o n s space o f space t h e space m e a n.

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    The normal distribution is also classified as

    p r o p e r t i e s space o f space n o r m a l space d i s t r i b u t i o n colon

rightwards double arrow i t space i s space a space b e l l space s h a p e d space c u r v e
rightwards double arrow T h e space m e a n comma space m o d e space a n d space m e d i a n space a r e space a l l space e q u a l. space
rightwards double arrow i t space i s space s y m m e t r i c space a b o u t space t h e space m e a n comma space mu.
rightwards double arrow space T h e space t o t a l space a r e a space u n d e r space t h e space c u r v e space i s space 1.
rightwards double arrow 68 percent sign space o f space t h e space d a t a space f a l l s space w i t h i n space 1 space s tan d a r d space d e v i a t i o n.
rightwards double arrow space 99.7 percent sign space o f space d a t a space o b s e r v e d space f o l l o w i n g space a space n o r m a l space d i s t r i b u t i o n space l i e s space w i t h i n space 3 space s tan d a r d space d e v i a t i o n s space o f space t h e space m e a n.

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    p r o p e r t i e s space o f space n o r m a l space d i s t r i b u t i o n colon

rightwards double arrow i t space i s space a space b e l l space s h a p e d space c u r v e
rightwards double arrow T h e space m e a n comma space m o d e space a n d space m e d i a n space a r e space a l l space e q u a l. space
rightwards double arrow i t space i s space s y m m e t r i c space a b o u t space t h e space m e a n comma space mu.
rightwards double arrow space T h e space t o t a l space a r e a space u n d e r space t h e space c u r v e space i s space 1.
rightwards double arrow 68 percent sign space o f space t h e space d a t a space f a l l s space w i t h i n space 1 space s tan d a r d space d e v i a t i o n.
rightwards double arrow space 99.7 percent sign space o f space d a t a space o b s e r v e d space f o l l o w i n g space a space n o r m a l space d i s t r i b u t i o n space l i e s space w i t h i n space 3 space s tan d a r d space d e v i a t i o n s space o f space t h e space m e a n.

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    p r o p e r t i e s space o f space n o r m a l space d i s t r i b u t i o n colon

rightwards double arrow i t space i s space a space b e l l space s h a p e d space c u r v e
rightwards double arrow T h e space m e a n comma space m o d e space a n d space m e d i a n space a r e space a l l space e q u a l. space
rightwards double arrow i t space i s space s y m m e t r i c space a b o u t space t h e space m e a n comma space mu.
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rightwards double arrow 68 percent sign space o f space t h e space d a t a space f a l l s space w i t h i n space 1 space s tan d a r d space d e v i a t i o n.
rightwards double arrow space 99.7 percent sign space o f space d a t a space o b s e r v e d space f o l l o w i n g space a space n o r m a l space d i s t r i b u t i o n space l i e s space w i t h i n space 3 space s tan d a r d space d e v i a t i o n s space o f space t h e space m e a n.

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    p r o p e r t i e s space o f space n o r m a l space d i s t r i b u t i o n colon

rightwards double arrow i t space i s space a space b e l l space s h a p e d space c u r v e
rightwards double arrow T h e space m e a n comma space m o d e space a n d space m e d i a n space a r e space a l l space e q u a l. space
rightwards double arrow i t space i s space s y m m e t r i c space a b o u t space t h e space m e a n comma space mu.
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T h i s space i s space w h y space t h i s space d i s t r i b u t i o n space i s space a l s o space k n o w n space a s space a space apostrophe n o r m a l space c u r v e apostrophe space o r space apostrophe b e l l space c u r v e apostrophe.

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    A space n o r m a l space d i s t r i b u t i o n space i s space a space t r u e space s y m m e t r i c space d i s t r i b u t i o n left parenthesis b e l l space s h a p e space g r a p h right parenthesis space m e a n s space comma space m o d e space a n d space m e d i a n s space a r e space e q u a l comma
W h e n space a space h i s t o g r a m space i s space c o n s t r u c t e d space o n space v a l u e s space t h a t space a r e space n o r m a l l y space d i s t r i b u t e d comma space t h e space s h a p e space o f space c o l u m n s space f o r m space a space s y m m e t r i c a l space b e l l space s h a p e.
T h i s space i s space w h y space t h i s space d i s t r i b u t i o n space i s space a l s o space k n o w n space a s space a space apostrophe n o r m a l space c u r v e apostrophe space o r space apostrophe b e l l space c u r v e apostrophe.

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