SOLUTION: Stress at work: In a poll conducted by the General Social Survey, 81% of respondents said that their jobs were sometimes or always stressful. Two hundred workers are chosen at ra

Question 1151818: Stress at work: In a poll conducted by the General Social Survey, 81% of
respondents said that their jobs were sometimes or always stressful. Two hundred
workers are chosen at random.
Approximate the probability that 160 or fewer find their jobs stressful.

Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
Stress at work: In a poll conducted by the General Social Survey, 81% of
respondents said that their jobs were sometimes or always stressful. Two hundred
workers are chosen at random.

This is a binomial problem, number of trials = n = 200,
probability of "success" in one trial = p = 81% = 0.81

m = n∙p = 200∙0.81 = 162



We use the normal to approximate the binomial.

Since we are including 160 ("160 or less") and since it is "or less",
we consider the upper limit to be 0.5 more than 160, or 160.5.



Round to two decimals -0.36 

There are two kinds of tables in use today. 

If your table is like this one, giving all the area to the left of z,

http://www.z-table.com/

scroll down to find -0.3 in the left-most z-column, then go over to the column headed 0.06, and read 0.3594

If your table is like this one, giving area to the right of 0,

https://www.mathsisfun.com/data/standard-normal-distribution-table.html

find 0.3 in the left-most z-column, then go over to the column headed
0.06, and read 0.1406.  Then subtract from 0.5 to get 0.3594

Or on your TI-83 or 84,

Press 2ND VARS

normalcdf(-1E99,-0.3604920469,0,1)

Press ENTER

Read 0.3592396598, which differs in the 4th place because the calculator
is more accurate than old-fashioned tables, which nobody but old-fashioned
teachers use anymore. lol

Edwin

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