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Normal Distribution · Question 42 of 68

What percentage of the city's girls are between 140 cm and 165 cm tall?

Question 42

MediumOriginal question

The heights of 15-year-old girls in a city are normally distributed with mean 150 cm and standard deviation 10 cm. (Take P(0<Z<0.5)=0.1915P(0 < Z < 0.5) = 0.1915, P(0<Z<1)=0.3413P(0 < Z < 1) = 0.3413, P(0<Z<1.5)=0.4332P(0 < Z < 1.5) = 0.4332 and P(0<Z<1.96)=0.4750P(0 < Z < 1.96) = 0.4750.)

What percentage of the city's girls are between 140 cm and 165 cm tall?

Options for question 42

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. z=−1z = -1 at 140 cm and z=1.5z = 1.5 at 165 cm, on opposite sides of the mean.

  2. 0.3413+0.4332=0.77450.3413 + 0.4332 = 0.7745, so 77.45%.

Worth noting

9.19% subtracts the areas, which is right only when both values lie on the same side of the mean.

Concept
A share across the mean
Typical time
120 s
Your time
—
The rule this testsAreas under the curve
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