In 2011, the Institute of Medicine (IOM), a non-profit group affiliated with the Select one US National Academy of Sciences, reviewed a study measuring bone quality 10 points 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. O Yes, there are at least 10 people with weak bones and 10 people with strong bones in each group. C. O No, the groups are not the same size. D. O No, there are not at least 10 people with weak bones and 10 people with strong bones in each group.

The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\frac{\sigma}{\sqrt{n}}[/tex]

The correct answer is:

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

Parrain Parrain · Answer 2 · 2022-04-12T16:59:24+02:00

As regards using the normal model, the correct answer is D. No, there are not at least 10 people with weak bones and 10 people with strong bones in each group.

Why can't the normal model be used?

In sampling distributions, the normal model can be used if np ≥ 10 and n (1 - p) ≥ 10.

In this case, those with weak bones are:

= 8.5% x 82

= 6.97 people which is less than 10

= 1% x 593

= 5.93 people

We do not have 10 or more people for the sample sizes so the normal model will not be a good fit.

Find out more on the normal model at https://brainly.com/question/15399601.