Mathematics
Grade10
Easy

Question

In the context of the z-score:
In test scores,

  1. Equal is better      
  2. Higher is better 
  3. Both a and b
  4. None of the above

The correct answer is: Higher is better


    h i g h e r space i s space b e t t e r comma space i s space c o r r e c t space c h o i c e

T h e space m a j o r space d i f f e r e n c e space b e t w e e n space u sin g space a space Z space s c o r e space a n d space a space T space s c o r e space i s.
space t h a t space y o u space h a v e space t o space e s t i m a t e space t h e space p o p u l a t i o n space s tan d a r d space d e v i a t i o n.
space T h e space T space s c o r e space i s space a l s o space u s e d space i f space y o u space h a v e space a space s m a l l space s a m p l e space s i z e space left parenthesis l e s s space t h a n space 30 right parenthesis.
space
Z space s c o r e space i s space t h e space s tan d a r d i z a t i o n space f r o m space t h e space p o p u l a t i o n space r a w space d a t a space o r space m o r e space t h a n space 30 space s a m p l e space d a t a space

    T h e space m a j o r space d i f f e r e n c e space b e t w e e n space u sin g space a space Z space s c o r e space a n d space a space T space s c o r e space i s.
space t h a t space y o u space h a v e space t o space e s t i m a t e space t h e space p o p u l a t i o n space s tan d a r d space d e v i a t i o n.
space T h e space T space s c o r e space i s space a l s o space u s e d space i f space y o u space h a v e space a space s m a l l space s a m p l e space s i z e space left parenthesis l e s s space t h a n space 30 right parenthesis.
space
Z space s c o r e space i s space t h e space s tan d a r d i z a t i o n space f r o m space t h e space p o p u l a t i o n space r a w space d a t a space o r space m o r e space t h a n space 30 space s a m p l e space d a t a space

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    Maha and Arjun are comparing scores on their college entrance exams. Maha’s SAT score is 1400. Arjun’s ACT score is 40. The mean SAT score is 1100 with a standard deviation of 200. The mean ACT score is 20 with a standard deviation of 6.
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    The standardization of a random variable Suppose X is a random variable with mean µ and standard deviation σ > 0

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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
rightwards double arrow 95 percent sign space o f space d a t a space v a l u e space i n space a space n o r m a l space d i s t r i b u t i o n space w i t h i n space 2 space s tan d a r d space d e v i a t i o n 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
rightwards double arrow 95 percent sign space o f space d a t a space v a l u e space i n space a space n o r m a l space d i s t r i b u t i o n space w i t h i n space 2 space s tan d a r d space d e v i a t i o n 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

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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.
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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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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.
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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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    If the z-score of the normal distribution is 2.5, the mean of the distribution is 45 and the standard deviation of the normal distribution is 3 less than the value of the x for the normal distribution is

    Use straight z minus score equals fraction numerator text  data value  end text minus text  mean  end text over denominator text  Standard deviation  end text end fraction

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    Use formula Z = (X −µ)/σ

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    Use formula Z = (X −µ)/σ

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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.

    The normal distribution is also classified as

    MathematicsGrade10

    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 area under a standard normal curve is ______

    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.

    The area under a standard normal curve is ______

    MathematicsGrade10

    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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    Grade10
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    For a standard normal variate, the value of the standard deviation is ____

    For a standard normal variate, the value of the standard deviation is ____

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    For a normal distribution its mean, median, mode are equal.

    For a normal distribution its mean, median, mode are equal.

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    Skewness of normal distribution is ______

    Skewness of normal distribution is ______

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