a)
Check the picture below.
b)
volume wise, we know the smaller pyramid is 1/8 th of the whole pyramid, so the volume of the whole pyramid must be 8/8 th.
Now, if we take off 1/8 th of the volume of whole pyramid, what the whole pyramid is left with is 7/8 th of its total volume, and that 7/8 th is the truncated part, because the 1/8 we chopped off from it, is the volume of the tiny pyramid atop.
Now, what's the ratio of the tiny pyramid to the truncated bottom?
Answer:
Z scores between -0.995 and 0.995 bound the middle 68% of the area under the stanrard normal curve
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Middle 68%
Between the 50 - (68/2) = 16th percentile and the 50 + (68/2) = 84th percentile.
16th percentile:
X when Z has a pvalue of 0.16. So X when Z = -0.995
84th percentile:
X when Z has a pvalue of 0.84. So X when Z = 0.995.
Z scores between -0.995 and 0.995 bound the middle 68% of the area under the stanrard normal curve