Respuesta :
GIVEN:
We are told that ten rugby balls are randomly selected from the production line to see if their shape is correct.
Over time, the company has found that 92.4% of all their rugby balls have the correct shape.
Required;
If exactly 7 of the 10 have the right shape, should the company stop the production line?
Step-by-step solution;
The sample for this experiment size is 10, the number of successes is 7 and the probability is 0.924.
In order to solve this problem we shall apply the binomial distribution formula which;
[tex]P(x)=(_x^{_n})P^x(1-P)^{n-x}[/tex]Now we substitute the given values and we'll have;
[tex]\begin{gathered} P(x=7)=(_7^{10})\times(0.924)^7\times(1-0.924)^{10-7} \\ \\ P(x=7)=120\times0.575047604381\times0.000438976 \\ \\ P(x=7)=0.0302918516617 \\ \\ P(x=7)\approx0.0303 \end{gathered}[/tex]Notice that this is less than 0.05, that is;
[tex]0.0303<0.05[/tex]This probability is unsual. Hence,
ANSWER: Yes the company should stop the production line since the probabilty of 7 balls having the correct shape is unusual.
