SOLUTION: Survey is 40% random sample is 250 we need to find the probability Exactly 95 Between 105 and 110 At most 85 At least 95 for at least 95 you subtract 1 and did 94 but how is t

Question 1131283: Survey is 40% random sample is 250 we need to find the probability
Exactly 95
Between 105 and 110
At most 85
At least 95 for at least 95 you subtract 1 and did 94 but how is that possible when at least 95 will be 95 up to 250?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
If the probability is exactly 40%, then the mean is np=100 and the variance np(1-p) or 100*.6=24 and the sd sqrt (24)=4.90
exactly 95 is 250C95*.4^95*.6^155=0.0421
using normal approximation, this is (94.5-100)/4.90 and (95.5-100)/4.9 or z between -1.12 and -0.92 for a probability of 0.0474
between 105 and 110 I would use the normal approximation using 105.5 and 109.5 unless it included 105 and 110, and then I would use 104.5 and 110.5. There are two possible answers. Using the first, it would be
z=(105.5-100)/4.9 or +1.12 and z=9.5/4.9 or 1.94
This has a probability of 0.1052
at most 85 is z < (84.5-100)/4.9 or z<=-3.16 and probability of 0.0008
at least 95, I would use (94.5-100)/4.9 or z>-1.12 which is 0.8686
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