The only condition that is not appropriate to assume that the sampling distribution of the sample mean is approximately normal is;
C: A random sample of 10 taken from a population distribution that is skewed to the right.
Now, looking at the given options below, we see that the random samples in options A and B are normally distributed and so their sample mean will be approximately normal.
Similarly, Option E shows that the population is uniform and so the sample mean will also be approximately normal.
Now, options C and D are skewed to the right and left respectively but option C has a sample size not greater 10 and as such it's sample mean will not be approximately normal
The missing options are;
A) A random sample of 8 taken from a normally distributed population.
B) A random sample of 50 taken from a normally distributed population.
C) A random sample of 10 taken from a population distribution that is skewed to the right.
D) A random sample of 75 taken from a population distribution that is skewed to the left.
E) A random sample of 100 taken from a population that is uniform.
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