EduFarming
Your list · 0हिं

Type at least two letters. Press Esc to close.

↑↓ navigate↵ openTAB cycle filter

Normal Distribution · Question 41 of 68

What percentage of the city's girls are shorter than 145 cm?

Question 41

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 shorter than 145 cm?

Options for question 41

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. z=145−15010=−0.5z = \frac{145 - 150}{10} = -0.5.

  2. P(Z<−0.5)=0.5−0.1915=0.3085P(Z < -0.5) = 0.5 - 0.1915 = 0.3085, so 30.85%.

Worth noting

19.15% is the share between 145 cm and the mean.

Concept
The share below a value
Typical time
120 s
Your time
—
The rule this testsAreas under the curve
Practise this chapter →

Ten questions from Normal Distribution, at your own pace.

Practise this chapter →

Ten questions from Normal Distribution, at your own pace.

Practise this chapterAll 68 questions in Normal DistributionRevise the notes for Normal Distribution