CAIE A-Level Mathematics 5.5.2 Problems with a Normal Variable

CAIE A-Level Mathematics 5.5.2 Problems with a Normal Variable
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise standardising a normal variable to calculate probabilities and expected frequencies or working backwards from a probability to determine an unknown mean, deviation or…

How this is tested

  • write Z = (X − μ)/σ with each boundary substituted before consulting normal tables
  • combine Φ values or complementary tails to calculate an interval probability or expected count
  • convert a stated probability to its z-value and solve the resulting equation for μ, σ or a boundary

Question 7

[Maximum number: 10]

The times taken by Obi to walk to work each morning are normally distributed with mean 14.8 minutes and standard deviation 1.5 minutes.

Obi walks to work 5 days a week for 45 weeks in a year.

Question 7(a)

(a)

Find the probability that, on a randomly chosen day, Obi takes more than 15.6 minutes to walk to work.

[ 3 ]

Question 7(b)

(b)

On 90%90\% of days, Obi takes more than t minutes to walk to work.

Find the value of t.

[ 3 ]

Question 7(c)

(c)

On how many days in a year would you expect Obi to take within one minute of the mean time to walk to work?

[ 4 ]