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?
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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