Question 1138943: Please help with this statistics question
In a survey conducted during the previous year by the World Council of
Engineers it was revealed that 16 out of a random sample of 64 of engineers
were female. It is assumed that the current rate is persisting worldwide. A sample of 1 000 engineers is selected
3.2.1 Calculate the probability that at most 375 of them will be female.
3.2.2 Calculate the probability that at least 420 of them will be female.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Use the Binomial Probability Formula,
:
Probability(P) (k successes in n trials) = nCk * p^k * (1-p)^(n-k), where nCk = n!/(k! * (n-k)!), p is probability of one success
:
For this problem p = 16/64 = 0.25, n = 1000
:
3.2.1 P(at most 375 will be female) = summation for k from 0 to 375 of 1000Ck * (1/4)^k * (1-(1/4))^(1000-k) = 0.999999
:
3.2.2 P(at least 420 of them will be female) = summation for k from 420 to 1000 of 1000Ck * (1/4)^k * (1-(1/4))^(1000-k) = 0.000001
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