Main answer
The probability that the sample mean time between the last drink and the onset of withdrawal will be 38 hours or more is approximately 0.2975
Step-by-step explanation
To find the probability that the sample mean time between the last drink and the onset of withdrawal will be 38 hours or more, we need to calculate the z-score and find the corresponding probability using the standard normal distribution.
Given:
Mean (μ) = 39.5 hours
Standard deviation (σ) = 17 hours
Sample size (n) = 34
First, calculate the standard error of the mean (SE) using the formula:
SE = σ /
(n)
SE = 17 /
(34)
SE ≈ 2.9187
Next, calculate the z-score using the formula:
z = (X - μ) / SE
X = 38 hours
z = (38 - 39.5) / 2.9187
z ≈ -0.5143
Now, find the probability corresponding to this z-score using a standard normal distribution table or a calculator.
Using a standard normal distribution table, the probability corresponding to a z-score of -0.5143 is approximately 0.2975.
Therefore, the probability that the sample mean time between the last drink and the onset of withdrawal will be 38 hours or more is approximately 0.2975.
Alcohol withdrawal occurs when a person who uses alcohol excessively suddenly stops the alcohol use. Studies have shown that the onset of withdrawal is experienced a mean of 39.5 hours after the last drink, with a standard deviation of 17 hours. A sample of 34 people who use alcohol excessively is to be taken. What is the probability that the sample mean time between the last drink and the onset of withdrawal will be 38 hours or more? carry your intermediate computations to at least four decimal places. round your answer to at least three decimal