Hello, I am wondering if someone could help me with these questions. I am having

Question

Hello, I am wondering if someone could help me with these questions. I am having a hard time understanding this assignment. Thank you in advance. Suppose you are working with a data set in which the mean = 45, and the standard deviation = 8 1. 1. What proportion of scores lie between the mean and z = 1.65? 2. What proportion of scores lie between the mean and z = -1.96? 3. What z score represents the 35th percentile? 4. What z score represents the 15th percentile? 5. What raw score represents the 35th percentile? 6. What raw score represents the 15th percentile? 7. What proportion of scores are between the 15th and 35th percentile? 8. What proportion of scores are between the 49th percentile and a z score of .85?

Explanation / Answer

1) Mean has a z score of 0
P(0 < Z < 1.65) = P(Z < 1.65) - P(Z < 0) = 0.9505 - 0.5 = 0.4505

2) P(-1.96 < Z < 0) = P(Z < 0) - P(Z < -1.96) = 0.5 - 0.0287 = 0.4713

3) P(Z < z) = 0.35
Use z table to find the z value correspong to a p value of 0.35
Z = -0.39

4) P(Z < z) = 0.15
Z = -1.04

5) P(Z < z) = 0.35
Z = -0.39
Z = (x - mean)/std. dev.
-0.39 = (x - 45)/8, x = 41.88

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