Central Limit Theorem and Probabilities Under Standard Normal Curve

Will you check my work on 1, 2 & 5 and then help me with 3, 4 & 6... I don't know if the formula is still the same for all of them or different.

1. The heights of eighteen-year-old men are approximately normally distributed with a mean (µ) of 68 inches and a standard deviation (σ) of 3 inches. What is the probability that an eighteen-year-old man selected at random is taller than 70 inches?
Z= 70-68 0.6667
3
2. Suppose that, instead of randomly selecting one 18-year-old male, you randomly select ten 18-year-old males. What is the probability that the average height for these 18-year-old males is more than 70 inches?
Z= 70-68 2.1 = 2.1 0.4821
3/√10

3. 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?

4. What would the average be for all sample means from samples of this size?

5. What would the standard error be for all sample means from samples of this size?
2.5/√40 = 0.40

6. 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?

Solution Preview

1. The heights of eighteen-year-old men are approximately normally distributed with a mean (µ) of 68 inches and a standard deviation (σ) of 3 inches. What is the probability that an eighteen-year-old man selected at random is taller than 70 inches?
Z=(70-68)/[3]=0.6667. Probability=P(Z>0.67)=0.2514

2. Suppose that, instead of randomly selecting one 18-year-old male, you randomly ...

Solution Summary

The solution gives detailed steps on computing probabilities either under standard normal curve or applying the central limit theorem.

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http://www.tandfonline.com/doi/abs/10.1080/02664761003692308?journalCode=cjas20#.UdSZ1fnVCuk

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