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Normal Distribution · Question 65 of 68

Question 65

HardOriginal question

Marks are normal with mean 65 and standard deviation 7. The top 2.28% of students get an A. What is the least mark for an A? (Take P(0<Z<2)=0.4772P(0 < Z < 2) = 0.4772.)

Options for question 65

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. A tail of 2.28% means P(Z>z)=0.0228=0.5−0.4772P(Z > z) = 0.0228 = 0.5 - 0.4772, so z=2z = 2.

  2. x=65+2×7=79x = 65 + 2 \times 7 = 79.

Worth noting

51 goes 2 standard deviations below the mean: that marks the bottom 2.28%.

Concept
A cut-off from a percentage
Typical time
120 s
Your time
—
The rule this testsUsing the normal distribution
Practise this chapter →

Ten questions from Normal Distribution, at your own pace.

Practise this chapter →

Ten questions from Normal Distribution, at your own pace.