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11 February, 02:31

The heights of different flowers in a field are normally distributed with a mean of 12.7 centimeters and a standard deviation of 2.3 centimeters.

What is the height of a flower in the field with a z-score of 0.4?

Enter your answer, rounded to the nearest tenth, in the box.

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  1. 11 February, 02:48
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    Answer: the height of a flower in the field is 13.6 centimeters.

    Step-by-step explanation:

    Since the heights of different flowers in a field are normally distributed, we would apply the formula for normal distribution which is expressed as

    z = (x - µ) / σ

    Where

    x = heights of different flowers.

    µ = mean height

    σ = standard deviation

    From the information given,

    µ = 12.7 centimeters

    σ = 2.3 centimeters

    The z-score is 0.4

    Therefore,

    0.4 = (x - 12.7) / 2.3

    Cross multiplying by 2.3, it becomes

    0.4 * 2.3 = x - 12.7

    0.92 = x - 12.7

    x = 0.92 + 12.7

    x = 13.6 centimeters to the nearest tenth
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