1 . This question aims at investigating the performance of three athletes in a 100 metres running practice .
In January 2021 , Patty , Quinn and Rachel are three athletes belonging to the same running group . It is given that the time for Patty , Quinn and Rachel to finish a 100 metres run are normally distributed , with means and standard deviations as follows :
Athlete |
Patty |
Quinn |
Rachel |
Variable |
P |
Q |
R |
Mean |
14.1s |
14.9 s |
� s |
Standard deviation |
0.7 s |
0.55 s |
� s |
Assume that the time for each of them to finish a 100 metres run are independent of each other .
On one training day , Patty practiced 100 metres run for three times , and the times used are recorded .
( a ) Write down , for the sum of the three observations ,
( i ) the mean ;
( ii ) the variance .
( b ) Hence , find the probability that Patty used less than 40.5 seconds in total .
On another training day , Patty and Quinn both practiced 100 metres run for five times , and the times used are recorded .
( c ) Find the variance for the mean of
( i ) Patty ’ s trials ;
[ 2 ]
[ 2 ]
( ii ) Quinn ’ s trials .
( d ) Hence , find the probability that the mean time for Patty ’ s five trials is
[ 4 ]
( i ) greater than that for Quinn ’ s five trials ;
( ii ) 0.2 seconds within that for Quinn ’ s five trials . [ 8 ]
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