1. What is the area under a standard normal curve? Why is it that number?
2. A statistics student was about to hand in some homework when his friend pointed at his answers and said, “You may want to recheck those.” The friend saw this:
The probability of the event is
a. -1/3
b. 1.5
c. 0.27
d. 0
e. 1
3.Examine the bell-shaped curves below and answer the questions.
The picture above is the Standard Normal Distribution. Where is the mean on that curve?
The picture above is the Standard Normal Distribution. Where is the median on that curve?
The picture above is the Standard Normal Distribution. Where is the mode on that curve?
Look at the picture of the different curves in the picture above. What happens to the height of the curve as the standard deviation increases?
4.Explain how to compute the z value. Start with the formula. Tell us what each variable means. Then, explain what the z value tells us about the value of the random variable. Use the numbers in 5a (below) to aid in your explanation.
5.Let x be a normally distributed random variable with µ=32 and σ=2.17. Find the z value for each of the following observed values of x: Round to TWO decimal places if needed. Show your work.
a.X = 35
b.X = 30
c.X = 34.17
d. X = 28.2
e. X = 32.15
6. In #5,
a. which response (a, b, c, d, e) is the most uncommon due to how far it is from the mean?
b. which response(s) are within one standard deviation of the mean? How do you know?
7.If the random variable z has a standard normal distribution, sketch (insert your photos of your sketches) and find each of the following probabilities using a z table. You may need to reference an online z table.
a.P( -1.66 < z <0.15) b.P( z < 1.29) c.P( z > – 2.04)
Begin your sketch with a drawing of the standard normal distribution pictured below: