Normal distribution/probability

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5.Week_5NormalDistribution_Math225N11.xlsx
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Normal probability

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ANSWER
Z score x 3.5 Z score -2
mean 6.5
standard deviation 1.5
LESS THAN(At most) AREA LESS THAN ENTER Z score 0.8
Asked to find x 32 Probability Less than F7 0.7881
Mean 28
Stdev 5
MORE THAN (at least) AREA MORE THAN ENTER Z score -0.6666666667
Asked to find x 12 Probability more than F13 0.7475
Mean 14
Stdev 3
Probability INBETWEEN ENTER ANSWER
INBETWEEN Asked to find Large value 370 Probability between F19 and F20 is 0.6904
Asked to find smaller value 360
Mean 365.45
Stdev 4.9

Find x given probability

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Find x given Area to Right or Left Enter
Area to the left no If area to the left is given enter yes; otherwise say no
Area 0.03 enter decimal SUMMARY
Enter Mean 47500 z 1.8807936082
Enter Standard deviation 3000 Find x 53142.3808244538
Find X given Area in the middle
Area 0.5 enter decimal SUMMARY
Enter Mean 81 Lower x 78.3020409992
Enter Standard deviation 4 Upper x 83.6979590008

Empirical Rule

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ANSWER
Empirical Rule 68-95-99.7
mean 92 Lower number Upper number
standard deviation 13 68% 79 105
95% 66 118
99.70% 53 131

CLT Theorem

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CLT THEOREM FOR MEANS Standard error 2.8366
n 10
Standard deviation 8.97
CLT THEOREM FOR PROPORTION Standard error 0.0913
n 30
proportion of success 0.5