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Normal Distribution · Question 68 of 68

The app wants to promise a delivery time that only 5% of its deliveries exceed.

Question 68

HardOriginal question

A food-delivery app's delivery times are normally distributed with mean 40 minutes and standard deviation 8 minutes. (Take P(0<Z<0.5)=0.1915P(0 < Z < 0.5) = 0.1915, P(0<Z<0.75)=0.2734P(0 < Z < 0.75) = 0.2734, P(0<Z<1.645)=0.45P(0 < Z < 1.645) = 0.45 and P(0<Z<2)=0.4772P(0 < Z < 2) = 0.4772.)

The app wants to promise a delivery time that only 5% of its deliveries exceed. What time should it promise?

Options for question 68

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. The top 5% lie above z=1.645z = 1.645, since 0.5−0.45=0.050.5 - 0.45 = 0.05.

  2. 40+1.645×8=53.1640 + 1.645 \times 8 = 53.16 minutes.

Worth noting

55.68 minutes uses z=1.96z = 1.96, which leaves 2.5% above.

Concept
A cut-off from a tail share
Typical time
150 s
Your time
—
The rule this testsUsing the normal distribution
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