Probability based on Z score 1 For a sample selected from a population with a mean of Âµ=50 and a st

Probability based on Z score

1 For a sample selected from a population with a mean of
Âµ=50 and a standard deviation of σ = 10:

a What is the expected value of M and the standard error of
M for a sample of n=4 scores?

b What is the expected value of M and the standard error of
M for a sample of n = 25 scores?

2 A population has a mean of Âµ = 80 and a standard
deviation of σ = 10 If you selected a random sample of n = 25 scores,
how much error would you expect between the sample mean and the population
mean?

3 A population forms a normal distribution with a mean of Âµ
= 75 and a standard deviation of σ = 20

Sketch the distribution of sample means for samples of n =
100 What proportion of the sample means for n = 100 have values greater than
79? In other words, find p(M>79) for n = 100

4 A normal-shaped distribution has Âµ=80 and σ =
15 Sketch the distribution of sample means for samples of n = 25 scores from
this population Compute the z-scores for M = 89 for a sample of n = 25 scores
Is this sample mean in the middle 95% of the distribution?