Suppose that the heights of male basketball players are normally distributed with an average of 70 inches and a variance of 4. What is the probability that a randomly selected male basketball player has a height that is in the range 69 inches to 72 inches?
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PROBLEM:
Suppose that the heights of male basketball players are normally distributed with an average of 70 inches and a variance of 4. What is the probability that a randomly selected male basketball player has a height that is in the range 69 inches to 72 inches?
SOLUTION:
Step 1: Identify the parts of the word problem. The word problem will identify:
Standard deviation is the square root of variance.
The height is in the range 69 inches to 72 inches thus they are between 68 and 73 inches.
Step 2: Figure out the z-scores and find the area in the z-table. Plug the X values into the z value formula and solve. The μ (the mean), is 70 inches.
See z-table and the graph (illustration) on the attached pictures.
Step 3: Add the computed z-scores to get the probability or area between -1 and 1.5. You can also convert them in percent.
ANSWER: