Question 878492
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Hi
I.  recommend using a TI Calculator for this summer school class ...
There are no excuses one can have for a poor grade.
Can recommend stattrek.com as an EXCELLENT reference (checking your TI results etc)
II. Must Learn when to recognize a Binomial Distribution, when You see one.
Most recognizable when You see a % of a certain event given.  Generally when samples are very Large(>1000), 
one uses a <u>normal approximation</u> to the binomial.
Trick is: When Using the normal <u>approxiamation</u>, one uses 'endpoints' (using .5)
a)p(error) = .10,  n = 4057, mean = 405.7 and SD = sqrt(405.7*.90) = 19.108
P(x > 409) = 1 - P(z &#8804; ({{{  highlight_green(409.5) }}}  - 405.7)/19.1084 = 1- P(z &#8804; .199) = 1 - .5789 = .4211
b) P(x &#8804; 409) = P(z &#8804; .199) = .5789
c) P(x = 409) = P(z &#8804; .199) -  P(z &#8804; ({{{  highlight_green(408.5) }}}  - 405.7)/19.1 = .5789 - .5583= .0206
Again, while it is not to 4 decimal points.. one can verify this using stattrek.com (Binomial distributions)
If Using TI...Using syntax:
normalcdf(-9999, 409.5, 405.7, 19.1) and normal(-999,408.5, 405.7, 19.1)
would have made short work of this