Final Answer:
There is a 98.81% probability that the phone volunteer will achieve her goal of an average donation of at least $100 from the 80 new members.
Step-by-step explanation:
Given Information:
Average donation goal: $100
Number of new members: 80
Population mean donation: $137.5
Population standard deviation: $16.61
Calculation Steps:
Calculate the standard error of the mean:
Standard error = Population standard deviation / Square root of sample size
Standard error = $16.61 / √80 = $2.08
Calculate the z-score of the average donation goal:
z-score = (Average donation goal - Population mean) / Standard error
z-score = ($100 - $137.5) / $2.08 = -2.26
Find the probability of the average donation exceeding the goal using a z-table:
Look up the area to the right of -2.26 in the z-table
Probability = 1 - 0.0119 = 0.9881
Therefore, based on the sampling distribution and the z-score, there is a 98.81% probability that the average donation for the 80 new members will be at least $100, allowing the volunteer to achieve her goal.
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Complete Question
One of the museum's phone volunteers sets a personal goal of getting an average donation of at least $100 from the new members she enrolls during the membership drive. If she gets 80 new members and they can be considered a random sample of all the museum's members, what is the probability that she can achieve her goal?
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