Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. find the value of the third quartile q3. round your answer to the nearest tenth.

The correct answer is:

65.3.

Explanation:

Q3 is the third quartile, and represents 75% of the data.  This means 75% of the data will fall below this value.  

Using a z-table, we see that the z-score associated with a probability of 0.75 is between 0.67 and 0.68; we will use 0.675.

The formula for a z-score is:
,

where X is our value, μ is the mean and σ is the standard deviation. 

We know that z = 0.675; μ is 63.6; and σ is 2.5:



Multiply both sides by 2.5:



Add 63.6 to both sides:
1.6875+63.6 = X-63.6+63.6
65.2875 = X
65.3 ≈≈ X

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