Question

Seven baseballs are randomly selected from the production line to see if their stitching is straight. Over time, the company has found that 89.4% of all their baseballs have straight stitching. If exactly five of the seven have straight stitching, should the company stop the production line

Answer 1

Answer:

The probability that exactly five of the seven have straight stitching is very low only 13.47%, this means that the company should stop the production line.

Step-by-step explanation:

We are given that Seven baseballs are randomly selected from the production line to see if their stitching is straight. Over time, the company has found that 89.4% of all their baseballs have straight stitching.

Let X = Number of baseballs having straight stitching

The above situation can be represented through the binomial distribution;

$P(X = r) = \binom{n}{r} \times p^{r}\times (1-p)^{n-r};x=0,1,2,3,.......$

where, n = number of samples (trials) taken = 7 baseballs

            r = number of success = exactly 5

            p = probbaility of success which in our question is the probability

                   that baseballs have straight stitching, i.e.; p = 89.4%

So, X ~ Binom(n = 7, p = 0.894)

Now, the probability that exactly five of the seven have straight stitching is given by = P(X = 5)

            P(X = 5) =  $\binom{7}{5} \times 0.894^{5}\times (1-0.894)^{7-5}$

                          =  $21 \times 0.894^{5}\times 0.106^{2}$

                          =  0.1347 or 13.47%

Since the probability that exactly five of the seven have straight stitching is very low only 13.47%, this means that company should stop the production line.