Question

Spin again Refer to Exercise 3. If only 7 of the 12 spins land in the blue region, do we have convincing evidence that the website's claim is false? Compute P(X < 7) with technology and use this result to support your answer.

Answer 1

To calculate the probability that fewer than 7 spins land in the blue region (i.e., P(X < 7)), we can use a binomial distribution. Assuming that each spin has a 60% chance of success (since 7 out of 12 spins land in the blue region), we can calculate it as follows:

P(X < 7) = Σ [from k = 0 to 6] from [12 choose k] * (0.6)^k * (0.4)^(12 - k)

Using a calculator or spreadsheet, we can calculate this. The exact value will be:

P(X < 7) ≈ 0.0337

If P(X < 7) is quite low, this suggests that only 7 of the 12 spins are unlikely to land in the blue region if the website's claim were true. Therefore, we could have convincing evidence that the website's claim is false, since the probability of this happening by chance is quite low.