Question

In 2011, the Institute of Medicine (IOM), a non-profit group affiliated with the US National Academy of Sciences, reviewed a study measuring bone quality and levels of vitamin-D in a random sample from bodies of 675 people who died in good health. 8.5% of the 82 bodies with low vitamin-D levels (below 50 nmol/L) had weak bones. Comparatively, 1% of the 593 bodies with regular vitamin-D levels had weak bones.

Is a normal model a good fit for the sampling distribution?

a)Yes, there are close to equal numbers in each group.

b)Yes, there are at least 10 people with weak bones and 10 people with strong bones in each group.

c)No, the groups are not the same size.

d)No, there are not at least 10 people with weak bones and 10 people with strong bones in each group.

I am thinking the answer is D due to the fact that if you multiply the 1% (.01)*593, you get the answer of 5.93. Leading to the conclusion that 5.93 is less than 10 and therefore would not be a good fit.

Please help! Thank you

Answer 1

D option

Yes, you are right

Remember the rule:

Rule of thumb is to use the normal approximation only if np>10 and np(1-p)>10.