SOLUTION: In each of the 118 independent observations, the event can occur with a probability of 0.19. Determine the probability that the event will occur between 20 and 50 times.

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Question 1198788: In each of the 118 independent observations, the event can occur with a probability of 0.19. Determine the probability that the event will occur between 20 and 50 times.
Answer by ikleyn(52880) About Me  (Show Source):
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In each of the 118 independent observations, the event can occur with a probability of 0.19.
Determine the probability that the event will occur between 20 and 50 times.
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This problem is on Binomial distribution

    n = 118 total trials;  p = 0.19 is the probability of an individual success;

    20 <= k <= 50 is the number of successful trials.


Since the number of trials is great, we use the normal distribution as an approximation.


The mean is  m = n*p = 118*0.19 = 22.42;  the standard deviation is  

    SD = sqrt%28n%2Ap%2A%281-p%29%29 = sqrt%28118%2A0.19%2A%281-0.19%29%29 = 4.26148  (rounded).


Now you can use your calculator

    p = normalcfd( 19.5, 50.5, 22.42, 4.26148) = 0.7534  (rounded).    ANSWER


The numbers 19.5 and 50.5 come with the continuity correction.

Solved.