Solve the problem. Round to the nearest tenth unless indicated otherwise.
-The amount of rainfall in January in a certain city is normally distributed with a mean of 4.5 inches and a standard deviation of 0.3 inches. Find the value of the quartile Q1.
A) 4.7
B) 1.1
C) 4.3
D) 4.4

Question

Quizplus · Accepted Answer

Q1 represents the 25th percentile, which means 25% of the data falls below Q1. To find Q1, we need to use a z-score table to find the z-score that corresponds to the 25th percentile.

Using the formula z = (x - μ) / σ and plugging in the values given in the problem, we get:

z = (x - 4.5) / 0.3

To find the z-score that corresponds to the 25th percentile, we look up the z-score for a cumulative probability of 0.25 in the z-score table, which is approximately -0.67.

Now we solve for x:

-0.67 = (x - 4.5) / 0.3
-0.201 = x - 4.5
x = 4.299

Rounding to the nearest tenth, we get 4.3. Therefore, the answer is C) 4.3.

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