Distribution

Question

A distribution has a mean of 50 and a standard deviation of 12.If we assume the above distribution is bell-shaped and symmetric what percentage of the observations will be between 26 and 74?

Answer 1

Bell shaped and symmetric does not mean normal. So any calculation assumming that it is is invalid.

 

Use chebychev's rule that states

AT LEAST 1-1/k² x 100% will be within 2 standard deviations

 

So at least 75%

Answer 2

The scores that you are talking about are 2 standard deviations below and 2 standard deviations above the mean.

 

What that means is your mean is 50. 1 standard deviation is 12 so 2 standard deviations is 24. 24 above 50 is 74 and 24 below 50 is 26. If you look at a normal table, which gives the percentages of people that fall within a specific range on a symmetric bell-shaped curve(normal curve), the table says that 47.72% of the people are 2 SDs above the mean and 47.72% of the people are 2 SDs below the mean.....so 95.44% of the people scored between 26 and 74.

 

Hope this helped