Suppose a random variable, x, arises from a binomial experiment. If n = 6, and p = 0.30, find the following probabilities using technology. a.) P (x=1) b.) P (x=5) c.) P (x=3) d.) P (x=less than equal 3) e.) P(x=greather than or equal 5) f.) P(x=less than or equal 4)
1 answer:
Answer:
<u> </u>
<u>a) P(X=1) = 0.302526 </u> <u>b) P(X=5) = 0.010206 </u> <u>c) P(X=3) = 0.18522 </u> <u>d) P(X≤3) = 0.92953 </u> <u>e) P(X≥5) = 0.010935 </u> <u>f) P(X≤4) = 0.989065 </u>
Explanation:
Binomial experiments are modeled by the formula:
Where
P(X=x) is the probability of exactly x successes
p is the probability of one success, which must be the same for every trial, and every trial must be independent of other trial. n is the number of trials 1 - p is the probability of fail there are only two possible outcomes for each trial: success or fail.
<u>a.) P (x=1) </u>
<u> </u>
<u>b.) P (x=5) </u>
<u>c.) P (x=3) </u>
Using the same formula:
<u>d.) P (x less than or equal to 3) </u>
P(X≤3)= P(X=3) + P(X=2) + P(X=1) + P(X=0)
Also,
P(X≤3) = 1 - P(X≥4) = 1 - P(X=4) - P(X=5) - P(X=6)
You can use either of those approaches. The result is the same.
Using the second one:
P(X=4) = 0.059335 P(X=5) = 0.010206 P(X=6) = 0.000729
P(X≤3) = 1 - 0.05935 - 0.010206 - 0.000729 = 0.92953
<u>e.) P(x greather than or equal to 5) </u>
P(X≥5) = 0.010206 + 0.000729 = 0.010935
<u>f.) P(x less than or equal 4) </u>
P(X≤4) = 1 - P(X≥5) = 1 - P(X=5) - P(X=6) P(X≤4) = 1 - 0.010206 - 0.000729 = 0.989065
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