Question

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.

Answer 1

Answer: the height of a flower in the field is 13.6 centimeters.

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