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Withdrawal symptoms may occur when a person using a painkiller suddenly stops using it. For a special type of painkiller, withdrawal symptoms occur in 4% of the cases.A random sample of 2400 people who have stopped using the painkiller is going to be taken. Let p be the proportion of people in the sample who experience withdrawal symptoms.Answer the following. (If necessary, consult a list of formulas.)(a)Find the mean of p.(b)Find the standard deviation of p.(c)Compute an approximation for P>p0.05, which is the probability that more than 5% of the people in the sample experience withdrawal symptoms. Round your answer to four decimal places.

Question

Withdrawal symptoms may occur when a person using a painkiller suddenly stops using it. For a special type of painkiller, withdrawal symptoms occur in 4% of the cases.A random sample of 2400 people who have stopped using the painkiller is going to be taken. Let p be the proportion of people in the sample who experience withdrawal symptoms.Answer the following. (If necessary, consult a list of formulas.)(a)Find the mean of p.(b)Find the standard deviation of p.(c)Compute an approximation for P>p0.05, which is the probability that more than 5% of the people in the sample experience withdrawal symptoms. Round your answer to four decimal places.

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Solution

(a) The mean of p is equal to the population proportion, which is 0.04.

(b) The standard deviation of p can be found using the formula sqrt[(P(1-P))/n], where P is the population proportion and n is the sample size. Substituting the given values, we get sqrt[(0.04*0.96)/2400] = 0.00308.

(c) To find P>p0.05, we first find the z-score using the formula (p0 - P) / standard deviation. Substituting the given values, we get (0.05 - 0.04) / 0.00308 = 3.25. Looking up this z-score in a standard normal distribution table, we find that the area to the left of this z-score is 0.9994. Since we want the area to the right (which represents the probability that more than 5% of the people in the sample experience withdrawal symptoms), we subtract this value from 1. So, P>p0.05 = 1 - 0.9994 = 0.0006.

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