from the set of 1000 observatins known to be normaly distribued the mean is 534cm & sd is 13.5cm....
.how many observations are likely to exeed 561cm ? how many will be between 520.5cm & 547.5cm ? between what limit will the middle 50% of the observation lie?
On a normal a normal distribution curve 34.18% lie within one standard deviation above the mean and bellow the mean. 13.68% lie between one and two standard deviations. 2.1% lie between the two and three standard deviaitons.
If the standard deviation is 13.5 cm, then 561 would be 2 standard deviations. 1000 (50%-34.18%-13.68%)=21.4
Between 520.5 is three standard deviation less than the mean and 547.5 is one standard deviation from the mean. The number of observations would be 1000(13.68%+2.1%)=157.8
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