Question

Alice works at a health care facility. She has measured the hemoglobin levels of 200 people. The data follows a normal distribution with a mean of 14 g/dL and a standard deviation of 1.
From the given data, we can conclude that about (64 or 32) people have hemoglobin levels less than 13, and about (100 or 64) people have hemoglobin levels greater than 14. help please

Answer 1

You can approach this visually, recalling that a normal distribution with mean \(\mu\) looks like a bell curve with its peak centered at \(\mu\):

With 200 people in the sample, according to this distribution, 50% of the sample fall to either side of the mean. You can use this fact to answer the second question right away.

Alternatively, you can approach this in a somewhat more rigorous fashion. The first question asks for the proportion of people with levels less than 13, which can be expressed as a probability:
\[P(X<13)=P\left(\frac{X-14}{1}<\frac{13-14}{1}\right)=P(Z<-1)\]
This probability gives you the proportion of people with levels less than 13, so multiplying this proportion by 200 will tell you how many people in the sample have these levels. You can do the same for the second question.