Question

Problems 1-4 assume a normally distributed population with a mean = 48 and standard deviation = 5.

Be sure to sketch the curve, include formulas & work, round appropriately, and circle your final answer.

What percent of the scores fall: at or below 54? at or above 40?

What proportion of scores lie between 31 and 48? 31 and 54?

Suppose we took a sample of 5000 scores from this distribution. Of those 5000 scores, how many would you expect to lie between 31 and 48? Of those 5000 scores how many would you expect to lie between 31 and 54?

If you select one person at random from this population and find his/her score on this variable to be 63 would you be surprised (yes/no)? Why/why not?

Answer 1

Here we have a normally distributed population with a mean = 48 and standard deviation = 5. Let .

The percent of the scores fall: at or below 54 is

88.49% percent of the scores fall: at or below 54 .

The percent of the scores fall: above 40 is

94.52% percent of the scores fall: above 40

The proportion of scores lie between 31 and 48 is

The proportion of scores lie between 31 and 54 is

Of those 5000 scores, the number expected to lie between 31 and 48 is

Of those 5000 scores, the number expected to lie between 31 and 54 is

63 is above 3 standard deviations above mean . The chance is only 0.01%.

Surprised . Very unlikely.