Question

Assume that a procedure yields a binomial distribution with a trial repeated n = 8 times. Use either the binomial probability formula (or technology) to find the probability of k = 5 successes given the probability p = 0.31 of success on a single trial. (Report answer accurate to 4 decimal places.) P(X = k) = Submit Question Question 8 Assume that a procedure yields a binomial distribution with a trial repeated n = 15 times. Use either the binomial probability formula (or a technology like your calculator or StatCrunch) to find the probability of k = 3 successes given the probability q = 0.39 of failure on a single trial. Hint: First find the probability of a success, p. (Report answer accurate to 4 decimal places.) P(X = k) = Submit Question Question 9 Assume that a procedure yields a binomial distribution with a trial repeated n = 15 times. Use either the binomial probability formula (or technology) to find the probability of k = 11 successes given the probability p = 47% of success on a single trial. (Report answer accurate to 4 decimal places.) P(X = k)

Answer 1

Q1) The probability here is computed using the binomial probabiltiy function as:

P(X = 5) = (*)p"(1 – p)* (7)}*(1 –p)*-* = (6)0.31*(1 – 0.31)* = 0.0527

Therefore 0.0527 is the required probability here.

Q2) As q = 0.39 is the probability of failure here, therefore p = 1 - 0.39 = 0.61 is the probability of success here. Therefore the probability here is computed as:

P(X = 3) = (2.) p*(1 – p)* 15 3 70.61°(1 – 0.61)12 = 0.0013

Therefore 0.0013 is the required probability here.

Q3) The probability here is computed as:

$P(X = 3) = \binom{n}{k}p^k(1-p)^{n-k} = \binom{15}{11}0.47^{11}(1 - 0.47)^{4} =0.0266$

Therefore 0.0266 is the required probability here.