SOLUTION: A survey report states that 70% of adult women visit their doctors for a physical examination at least once in two years. If 20 adult women are randomly selected, find the probabil

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Question 545197: A survey report states that 70% of adult women visit their doctors for a physical examination at least once in two years. If 20 adult women are randomly selected, find the probability that fewer than 14 of them have had a physical examination in the past two years.

Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
A survey report states that 70% of adult women visit their doctors for a physical examination at least once in two years. If 20 adult women are randomly selected, find the probability that fewer than 14 of them have had a physical examination in the past two years.

There are several methods.  I will explain the first 2.
1. By a cumulative prabability table.
2. By a TI-84 calculator
3. By a computer program
4. By formula calculation (so much calculation would make this method impractical, but not impossible)

1. Find this cumulative probability table headed "n=20" in your book, or the
website http://www.statisticshowto.com/tables/binomial-distribution-table/
from which I copied and pasted it.  You must interpret the words 
"fewer than 14" as "13 or fewer", go down the column headed by "p=0.7" to
the row with "x=13" and read 0.392 which I have colored red and underlined: 


n=20
 p 
 x  0.05   0.1  0.15   0.2  0.25   0.3  0.35   0.4  0.45   0.5  0.55   0.6  0.65   0.7  0.75   0.8  0.85   0.9  0.95 

 0 0.358 0.122 0.039 0.012 0.003 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 

 1 0.736 0.392 0.176 0.069 0.024 0.008 0.002 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 

 2 0.925 0.677 0.405 0.206 0.091 0.035 0.012 0.004 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 

 3 0.984 0.867 0.648 0.411 0.225 0.107 0.044 0.016 0.005 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 

 4 0.997 0.957 0.830 0.630 0.415 0.238 0.118 0.051 0.019 0.006 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 

 5 1.000 0.989 0.933 0.804 0.617 0.416 0.245 0.126 0.055 0.021 0.006 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 

 6 1.000 0.998 0.978 0.913 0.786 0.608 0.417 0.250 0.130 0.058 0.021 0.006 0.002 0.000 0.000 0.000 0.000 0.000 0.000 

 7 1.000 1.000 0.994 0.968 0.898 0.772 0.601 0.416 0.252 0.132 0.058 0.021 0.006 0.001 0.000 0.000 0.000 0.000 0.000 

 8 1.000 1.000 0.999 0.990 0.959 0.887 0.762 0.596 0.414 0.252 0.131 0.057 0.020 0.005 0.001 0.000 0.000 0.000 0.000 

 9 1.000 1.000 1.000 0.997 0.986 0.952 0.878 0.755 0.591 0.412 0.249 0.128 0.053 0.017 0.004 0.001 0.000 0.000 0.000 

10 1.000 1.000 1.000 0.999 0.996 0.983 0.947 0.872 0.751 0.588 0.409 0.245 0.122 0.048 0.014 0.003 0.000 0.000 0.000 

11 1.000 1.000 1.000 1.000 0.999 0.995 0.980 0.943 0.869 0.748 0.586 0.404 0.238 0.113 0.041 0.010 0.001 0.000 0.000 

12 1.000 1.000 1.000 1.000 1.000 0.999 0.994 0.979 0.942 0.868 0.748 0.584 0.399 0.228 0.102 0.032 0.006 0.000 0.000 

13 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.994 0.979 0.942 0.870 0.750 0.583 0.392 0.214 0.087 0.022 0.002 0.000 

14 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.994 0.979 0.945 0.874 0.755 0.584 0.383 0.196 0.067 0.011 0.000 

15 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.994 0.981 0.949 0.882 0.762 0.585 0.370 0.170 0.043 0.003 

16 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.995 0.984 0.956 0.893 0.775 0.589 0.352 0.133 0.016 

17 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.996 0.988 0.965 0.909 0.794 0.595 0.323 0.075 

18 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.998 0.992 0.976 0.931 0.824 0.608 0.264 

19 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.997 0.988 0.961 0.878 0.642 

20 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 

-----------------------

2. By TI-84 (or TI-83) calculator:

(You must also interpret the words "fewer than 14" as "13 or fewer")

Press 2ND
Press VARS
scroll down to binomcdf(
Press ENTER

[If you have the newer version, set trials at 20, p at 0.7, x value at 13,
highlight Paste, Press ENTER]

If you have the older version you must type in the missing parts of this

binomcdf(20,0,7,
13)

but with either version that's what you must have on your screen.

Press ENTER

Read .3919901882, which rounds to the 0.392 that you read from the table.

Edwin
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