I have a question where I need to find the z-score but the only info im given is the Mean (µ) and the standard?
Im really struggling with my statistics homework and this question has stumped me for long enough so now Im asking for someones help:
The questions is:
For a normal distribution with a mean of µ = 80 and a standard deviation of ơ = 20, find the proportion of the population corresponding to each of the following scores.
a- Scores greater than 85
b- Scores less than 100
c- Scores between 70 and 90
I think it has to do with the z-score and the Unit Normal Table but I cant figure out the z -score based on the information im given? Thank you for your help!!
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First, go here, http://www.cs.washington.edu/homes/jrl/normal_cdf....
a.) z = (85 - 80)/20 = .25
Using a normal(0,1) CDF table, find .25. This is the probability that a score falls below 85. Since we want the probability for scores GREATER than 85, just take 1 - [this value] = 1 - .5987 = .4013
b.) z = (100 - 80)/20 = 1
Use the normal table again to find P(Z < 1). That's your answer right there.
c.) zb = (90 - 80)/20 = .5
za = (70 - 80)/20 = -.5
We need the probability that a value falls between 70 and 90. So, if I take the CDF of a normal up to .5 and subtract the CDF of a normal up to -.5, this is your answer.
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