Questions: A test for marijuana usage was tried on 191 subjects who did not use marijuana. The test result was wrong 7 times. a. Based on the available results, find the probability of a wrong test result for a person who does not use marijuana. b. Is it "unusual" for the test to be wrong for those not using marijuana? Consider an event to be unusual if its probability is less than or equal to 0.05. a. The probability that the test will be wrong is approximately . (Type an integer or decimal rounded to three decimal places as needed.)

A test for marijuana usage was tried on 191 subjects who did not use marijuana. The test result was wrong 7 times.
a. Based on the available results, find the probability of a wrong test result for a person who does not use marijuana.
b. Is it "unusual" for the test to be wrong for those not using marijuana?

Consider an event to be unusual if its probability is less than or equal to 0.05.
a. The probability that the test will be wrong is approximately .
(Type an integer or decimal rounded to three decimal places as needed.)

Transcript text: A test for marijuana usage was tried on 191 subjects who did not use marijuana. The test result was wrong 7 times. a. Based on the available results, find the probability of a wrong test result for a person who does not use marijuana. b. Is it "unusual" for the test to be wrong for those not using marijuana? Consider an event to be unusual if its probability is less than or equal to 0.05 . a. The probability that the test will be wrong is approximately $\square$ . (Type an integer or decimal rounded to three decimal places as needed.)

Solution

Solution Steps

Step 1: Calculate the Probability of a Wrong Test Result

To find the probability of a wrong test result for a person who does not use marijuana, we use the formula:

\[ P(X = 1) = \frac{\text{Number of wrong results}}{\text{Total subjects}} = \frac{7}{191} \approx 0.03664921465968586 \]

Rounding this to three decimal places, we have:

\[ P(X = 1) \approx 0.037 \]

Step 2: Determine if the Result is Unusual

An event is considered unusual if its probability is less than or equal to $0.05$. We have calculated:

\[ P(X = 1) \approx 0.03664921465968586 \]

Since $0.03664921465968586 \leq 0.05$, we conclude that it is unusual for the test to be wrong for those not using marijuana.

Final Answer

The probability that the test will be wrong is approximately $ \boxed{0.037} $. It is unusual for the test to be wrong for those not using marijuana, so the answer is "Yes".

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