Answer :
The number of cereal boxes which weigh between between 496 and 506 grams will be 68.
mean = 500 grams
standard deviation =3g
x1 = 496
x2 = 506
using the normal distribution table,
z-scores
= z = (x-m)/s
= 496 - 500 / 3
= -4 / 3
= - 1.33
and for x2
506 - 500 / 3
= 6/ 3
= 2
Therefore , the probability will be,
P(x2) - P( x1)
= 0.4772 - 0.0917
= 0.3855
This corresponds to 68.
A standard deviation is a measure of how widely distributed the data is in reference to the mean. A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out.
A standard deviation near 0 suggests that data points are close to the mean, whereas a high or low standard deviation indicates that data points are above or below the mean, respectively.
The curve on top of Image 7 is more spread out and hence has a higher standard deviation, whereas the curve below is more grouped around the mean and thus has a smaller standard deviation.
To learn mre about standard deviation
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