SOLUTION: The average age for employees at an amusement park is 24 years old with a standard deviation of 2.5 years. Suppose random samples of 40 employees are selected. What would the distr

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Question 1120184: The average age for employees at an amusement park is 24 years old with a standard deviation of 2.5 years. Suppose random samples of 40 employees are selected. What would the distribution of average ages from samples of this size look like? Why?

Use the above amusement park scenario to answer the following questions:
A) What would the average be for all sample means from samples of this size?
B) What would the standard error be for all sample means from samples of this size?
C) What is the probability if you randomly selected 40 employees and averaged their ages together that the sample mean would be between 23 and 25 years?

Answer by ViviNH14(2) (Show Source):
You can put this solution on YOUR website!
A) 24 years old
B) SD = 2.5/ sqrt(40) = 2.5/6.325 = 0.395
C) (23-24)/(2.5/ sqrt(40)) = -1/(2.5/6.325) = -1/0.395 = -2.5296
The z value shows an area of 0/0057
Since the 23 and 25 are symmetrical about 4 then Z = 2.596
2(0.0057) = 0.0114 is the probability not included
1 - 0.0114 = 0.9886
The probability is 98.86%