Question

A binomial probability experiment is conducted with the given parameters. Use technology to find the probability of x successes in the n independent trials of the experiment. n=9​, p=0.45​, x<4

Answer 1

Answer:

The probability of  successes   P( x < 4 ) = 0.36138

Step-by-step explanation:

Step(i):-

Given 'n'=9

The probability of success 'p' = 0.45

                                            q = 1-p = 1-0.45 = 0.55

Let 'X' be the random variable in Binomial distribution

$P(X=r) = n_{C_{r} } p^{r} q^{n-r}$

$n_{C_{r} } = \frac{n!}{(n-r)!r!}$

Step(ii):-

The probability of x successes in the n independent trials of the experiment

$P(x$

              = $= 9_{C_{0} } (0.45)^{0} (0.55)^{9-0}+9_{C_{1} } (0.45)^{1} (0.55)^{9-1}+9_{C_{2} } (0.45)^{2} (0.55)^{9-2}+9_{C_{3} } (0.45)^{3} (0.55)^{9-3}$By using factorial notation

$n_{C_{r} } = \frac{n!}{(n-r)!r!}$

$9_{C_{0} } = 1 , 9_{C_{1} } = 9 , 9_{C_{2} } = 36, 9_{C_{3} } = 84$

P( x < 4 ) = (0.55)⁹ + 9(0.45) (0.55)⁸ + 36 (0.45)² (0.55)⁷ +84 (0.45)³ (0.55)⁶

P( x < 4 ) = 0.004605+0.03391 + 0.1109855+ 0.21188

P( x < 4 ) = 0.36138

Final answer:-

The probability of  successes   P( x < 4 ) = 0.36138