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One in every three Americans believes that the U.S government should send a
mission to Mars. If n = 30 Americans are randomly selected, find the probability that
Part a. Exactly 8 out of these 30 selected Americans believe that the U.S government
should send a mission to Mars.
Part b. At least 8 out of these 30 selected Americans believe that the U.S government
should send a mission to Mars No need to show calculations - you can use software)
Part c. Use the Normal Distribution to find the approximate answer in Part b.
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(a) It is a typical binomial distribution problem.
The number of trials is n=30; the number of success trials is k=8;\
The probability of success for each individual trial is p=1/3.
Using standard designations, the probability is P = P(n=30; k=8; p=1/3).
To facilitate my calculations, I used online calculator at this site https://stattrek.com/online-calculator/binomial.aspx
It provides nice instructions and a convenient input and output for all relevant options/cases.
The resulting number is P = 0.1192 (rounded). ANSWER
(b) Use the same mantra.
The resulting number is P = P(n=30; k>=8; p=1/3) = 0.83321 (rounded). ANSWER
(c) The normal distribution approximation has the mean m= n*p = 30*(1/3) = 10
and standard deviation of SD = = = 2.582 (rounded).
Use the continuous correction factor to get
P = normalcfd(7.5, 9999, 10, 2.582) = 0.8335 (rounded). ANSWER
It is close enough to the value of 0.83321 from part (b).
Solved.