SOLUTION: What is the probability that a normal random variable with mean 6 and standard deviation 3 will fall between 5.7 and 7.5 ?

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Question 1150701: What is the probability that a normal random variable with mean 6 and
standard deviation 3 will fall between 5.7 and 7.5 ?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Z-score+=+%287.5+-+6%29%2F3=+1.5%2F3+=+0.5

Look up 0.5 on a z-table. The result is 0.6915. This means there is a 0.6915 probability the random variable will be below 7.5.

Z-score+=+%285.7+-+6%29%2F3+=+%28-0.3%29%2F3+=+-0.1

Look up -0.1 on a z-table. The result is 0.4602. The means there is a 0.4602 probability the random variable will be below 5.7.

The find the probability the random variable will be between 7.5 and 5.7, simply subtract the two probabilities we found (above) from one another:

0.6915+-+0.4602+=+0.2313

So, there is a 0.2313 probability the random variable will fall between 7.5+and 5.7.