Your Practice Set – Applications and Interpretation for IBDP Mathematics
68
Paper 1 – Central Limit Theorem
Example
The random variable X is defined such that E ( X ) � 20 and Var ( X ) � 6 . A random
sample of 50 observations is selected from the distribution of X . Let X be the mean of the sample . By using the central limit theorem ,
( a ) write down E ( X ) ;
( b ) find Var ( X ) ;
( c ) find P ( X � 19.7 ) .
[ 1 ]
[ 2 ]
[ 2 ]
Solution
( a ) |
20 |
A1 |
( b ) |
Var ( X
) Var ( X
) � n
|
|
|
6 Var ( X
) �
50
|
( A1 ) for substitution |
|
3 Var ( X
) �
25
|
A1 |
( c ) |
� 3
� X ~ N�20 ,
� � 25
�
|
( M1 ) for valid approach |
|
P( X �19.7 ) �
0.8067619307
|
|
|
P ( X � 19.7) � 08
. 07
|
A1 |
[ 1 ]
[ 2 ]
[ 2 ]
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