Question

A binomial experiment with probability of success p=0.84 and n=7 trials is conducted. What is the probability that the experiment results in 6 or more successes?Do not round your intermediate computations, and round your answer to three decimal places.

Answer 1

Given

p = 0.84

n = 7

x = 6 or more successes

The probability is given by:

`P=C_n^x\cdot p^x\cdot(1-p)^(n-x)`

Then, substitute the values:

`P=((7\cdot6\cdot5\cdot4\cdot3\cdot2)/(1\cdot2\cdot3\cdot4\cdot5\cdot6))\cdot0.84^6\cdot(1-0.84)^(7-6)`

Simplify:

`P=(7)\cdot0.84^6\cdot0.16^1=0.3934`

Round three decimal places is 0.393.

Answer: the probability is 0.393