IQ is known to follow a normal distribution with a mean of 100 and a standard deviation of 15. If we chose a sample of 10 people, explain in one or two sentences why the distribution would still be considered normal even though the amount of people were under 30.

Question

Kali Wright

Mathematics

23 September, 05:50

IQ is known to follow a normal distribution with a mean of 100 and a standard deviation of 15. If we chose a sample of 10 people, explain in one or two sentences why the distribution would still be considered normal even though the amount of people were under 30.

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Brogan Humphrey · Answer 1

Step-by-step explanation:

According to the central limit theorem, a distribution is said to be normal if the sample size is sufficiently large (usually n > 30) notwithstanding whether the source population is normal or skewed. But for a population that is normally distributed the theorem still holds true. for samples smaller than 30.

The shape of the sampling distribution changes with a sample size. For a large sample size, the sampling distribution starts to approximate a normal distribution.