SOLUTION: 80% = Yes 20% = No A)Sample of 15 Probability more than 4 but fewer than 8 = Yes B)Sample of 2000 Probability that more than 380 = No probabii

Question 1058350: 80% = Yes
20% = No
A)Sample of 15
Probability more than 4 but fewer than 8 = Yes

B)Sample of 2000
Probability that more than 380 = No
probabii

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Want probability of 5,6,7
15C5(.8)^5(.2)^10=3003*0.32768*0.0000001024=0.0001
15C6(.8^6)(.2)^9=0.0007
15C7(.8^7)(.2^8)=0.0035
Total is 0.0043.
This should be small, since the expected value is 12 and the variance 12*(0.2)=2.4, so Std dev. between 1.5 and 1.6. These values are 3-4+ sd below the mean.
-----------------------------
Treat as a normal distribution with mean np=400
Variance is np(1-p)=400(.8)=320
Std dev is sqrt (320)=17.89
probability it is >380 is
probability that z is > (x-mean)/sd=(380-400)/17.89=-1.11
That is 0.8682

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