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In a survey of first graders, their mean height was 49.9 inches with a standard deviation of 3.15 inches. Assuming the heights are normally distributed, what height represents the first quartile of these students? a. 46.75 inchesb. 47.77 inchesc. 52.02 inchesd. 43.60 inches

Respuesta :

Answer:

The answer is (b) 47.77 inches

Explanation:

The first quartile is the 25th percentile, which is where 25% of the data falls. Since the data is normally distributed, we will use the formula

[tex]z = \frac{height - mean}{sd}[/tex]

First step is to look up the z-value of 25% = 0.25 in the standard normal table. z-value of 0.25 ≈ -0.67.

Therefore, the height that represent the first quartile is given as [tex]height = z*sd + mean = (-0.67) (3.15) + 49.9[/tex] [tex]= 47.77[/tex].

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