Question

decide whether you can use the normal distribution to approximate the binomial distribution. if you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. if you cannot, explain why and use the binomial distribution to find the indicated probabilities. a survey of adults found that 9% say their favorite sport is auto racing. you randomly select 600 adults and ask them to name their favorite sport. complete parts (a) through (d). (d) identify any unusual events. explain. a. the event in part (c) is unusual because its probability is less than 0.05. b. the event in part (a) is unusual because its probability is less than 0.05. c. the event in part (b) is unusual because its probability is less than 0.05. d. there are no unusual events, because all of the probabilities are greater than 0.05.

Explanation:

Step1: Recall the definition of an unusual event

An event is considered unusual if its probability is less than \(0.05\).

Step2: Analyze each option

• Option A: If the probability of the event in part (c) is less than \(0.05\), then it is unusual.
• Option B: If the probability of the event in part (a) is less than \(0.05\), then it is unusual. But we don't know the probability of part (a) from the given information.
• Option C: If the probability of the event in part (b) is less than \(0.05\), then it is unusual. But we don't know the probability of part (b) from the given information.
• Option D: This is only correct if all probabilities (from parts (a), (b), (c)) are greater than \(0.05\). But we don't have that information. However, based on the problem - solving convention (assuming that if we are given an option about a specific part (like part (c)) and the rule of unusual event (\(P < 0.05\))), and since we are not given the actual probabilities of (a) and (b), but the option A is in line with the definition of an unusual event (\(P<0.05\))

Answer:

A. The event in part (c) is unusual because its probability is less than \(0.05\).