Respuesta :
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.
Normal Distribution
- For the sampling distribution of the sample mean to be approximately normal, it means that the population must be normally distributed and uniform or the sample size must be greater than 10.
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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