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Normal Distribution · Question 53 of 68

Question 53

MediumOriginal question

Heights of adults in a town are normal with mean 160 cm and standard deviation 5 cm. What percentage are between 155 cm and 170 cm? (Take P(0<Z<1)=0.3413P(0 < Z < 1) = 0.3413 and P(0<Z<2)=0.4772P(0 < Z < 2) = 0.4772.)

Options for question 53

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. z=155−1605=−1z = \frac{155 - 160}{5} = -1 and z=170−1605=2z = \frac{170 - 160}{5} = 2.

  2. P(−1<Z<2)=0.3413+0.4772=0.8185P(-1 < Z < 2) = 0.3413 + 0.4772 = 0.8185, so 81.85%.

Worth noting

68.26% is −1<Z<1-1 < Z < 1, which stops at 165 cm.

Concept
The share between two values
Typical time
90 s
Your time
—
The rule this testsUsing the normal distribution
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Ten questions from Normal Distribution, at your own pace.

Practise this chapter →

Ten questions from Normal Distribution, at your own pace.