In a particular school system, the distribution of the average IQ of students is

Question

In a particular school system, the distribution of the average IQ of students is right skewed with a mean of 120 and a standard deviation of12. A sample of 45 students is selected from the schools within the system. Which of the following is true? O 1) O 2) 12 The distribution of sample means is approximately normal with mean 120 and standard deviation V45 12 The distribution of sample mecans is approximately normal with mcan 120 and standard deviation 45 3) The distribution of sample means is approximately normal with man 120and standard deviation 12. O 4) The population distribution and the distribution of sample means will have identical shapes.

Explanation / Answer

1) option is correct

by central limit theorem if the sample of a normal population have a sample size more than 30 than the sample is also normally distributed with mean = mean of population and standard deviation equal to standard deviation of population divided by square-root of the sample size of sample.

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