Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 70
1 . The weight of a margarine block , in grams , produced in a production line is studied . A sample of 12 observations is recorded as below :
300 , 302 , 308 , 305 , 297 , 301 , 504 , 501 , 495 , 498 , 510 , 491
( a ) Find an unbiased estimate of the population mean . [ 2 ]
( b ) Find sn � 1. [ 2 ]
( c ) Construct a 99 % confidence interval for the population mean , giving the answer to two decimal places .
[ 2 ]
2 . The time to install a program , in seconds , for a group of computers is studied . A sample of 6 observations is recorded as below :
66 , 50 , 34 , 51 , 71 , 52
( a ) Find an unbiased estimate of the population mean .
2 2
It is given that the population variance is � � 1.01s .
[ 2 ]
( b ) Construct a 95 % confidence interval for the population mean , giving the answer to three decimal places .
[ 2 ]
3 . Suki frequently travels from home to cinema . On n randomly selected occasions the journey time t minutes was recorded . It is given that t � 20 minutes , � � 3 minutes and the total time used in these n journeys is 500 minutes .
( a ) Find n . [ 2 ]
( b ) Construct a 90 % confidence interval for the population mean , giving the answer to three decimal places .
[ 2 ] ( c ) Hence , write down the interval width of the confidence interval , giving the answer to three decimal places . [ 1 ]
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