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math word problem

Alice has measured the hemoglobin levels of 200 people. If the data follows a normal distribution with a mean of 10 and a standard deviation of 1, what can you conclude?
 
one of these is the answer but i dont know which one.
 
About 64 people have hemoglobin levels less than 9.

About 32 people have hemoglobin levels less than 9.

About 64 people have hemoglobin levels less than 8.

About 32 people have hemoglobin levels less than 8.
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1 Answer

Hi Cassandra! 
 
This question is designed to see how well you understand the concepts related to a Normal Distribution. 
Many times when we sample a large body of data (say the hemoglobin levels of 200 people) we find that it follows the pattern of a "bell curve" which in Statistics is called a Normal Distribution. This means that if I plot the hemoglobin level on the x-axis and the number of people on the y-axis, I will get a bell-shaped curve with the peak of the "bell" located at the mean value (hemoglobin 10).
 
The "standard deviation" of a Normal curve measures how spread out the bell - shape is. A larger Standard Deviation means a shorter broader curve, and a smaller Standard Deviation means a taller, narrower curve. 
 
The properties of a Normal Distribution tell us the following things :
  • About half of the people have a hemoglobin greater than the mean value, and about half have a hemoglobin less that the mean value (the Normal curve is symmetric) 
  • About 68% of the people have a hemoglobin level within one Standard Deviation of the mean,  that means that 68% of the 200 people will have a hemoglobin level between 9 and 11.
68% of 200 is 136 people. That means that everybody else, or 64 people, have either a hemoglobin less than 9 or greater than 11. AND since our distribution is symmetric, half of these people will have less than 9 and half will have more than 11.
 
This means 32 people have a hemoglobin less than 9. 
 
A great website to review these topics is 
 
 
Hope this helps!