Question

Please help! Correct answer only!

Answer 1

Answer:

The probability that exactly 11 of the chosen clay objects are vases

P(X = 11 ) = 0.16472

Step-by-step explanation:

Step(i):-

Given students created 19 clay objects, 12 of which were vases

probability of successes

                            $p = \frac{x}{n} = \frac{12}{19} = 0.6315$

q  = 1 - p = 1 - 0.6315 = 0.3685

Step(ii):-

Given  n = 16

Let 'X' be the random variable in binomial distribution

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

The probability that exactly 11 of the chosen clay objects are vases

$P(X = 11) = 16 _{C_{11} } (0.6315)^{11} (0.3585)^{16-11}$

we will use formula

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

$n_{C_{r} } =n_{C_{n-r} }$

$16_{C_{11} } =16_{C_{16-11} }= 16_{C_{5} } = \frac{16 X 15 X 14 X 13 X 12}{5 X 4 X 3 X 2 X 1} = 4368$

$P(X = 11) = 4368 (0.006369)(0.005921)$

P(X = 11 ) = 0.16472

Conclusion:-

The probability that exactly 11 of the chosen clay objects are vases

P(X = 11 ) = 0.16472