What is scientific notation? Why is it useful? How is it used in the real world?
2 answers:
Very big and very small numbers are hard to write down because of all the zeroes and they're also hard to quickly evaluate and compare.
Instead of using a long sequence of decimal digits to represent numbers, scientific notation uses a shorter number multiplied by a power of 10 and it's always in that form and if it's not, it's not in proper scientific notation.
Scientific notation uses positive exponents to represent very large numbers and negative exponents to represent very small numbers.
I have attached an image which shows what scientific can be used for and an example of a number written in scientific notation.
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Answer:
The child's reading level is at the 3.4th percentile.
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.
You do some research and determine that the reading rates for their grade level are normally distributed with a mean of 90 words per minute and a standard deviation of 24 words per minute.
This means that
You find an individual that reads 46.4 word per minute. At what percentile is the child's reading level?
The percentile is the p-value of Z when X = 46.4, multiplied by 100. So
has a p-value of 0.034.
0.034*100 = 3.4
The child's reading level is at the 3.4th percentile.