CAIE A-Level Mathematics 5.5 Normal Distribution Question Bank

CAIE A-Level Mathematics 5.5 Normal Distribution Question Bank
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise direct and inverse normal calculations and normal approximations to binomial counts with continuity correction.

Exam points

  • standardise a normal variable or use calculator normal CDF for a tail or interval
  • use inverse normal probabilities to find a cut-off, mean or standard deviation
  • approximate a binomial with N(np,npq) and apply the correct continuity correction

Covered syllabus points

5.5.1—Normal distribution5.5.2—Problems concerning a variable X5.5.3—Binomial distribution

Question 5(b)

[Maximum number: 5]

On any given day, Cooper either wears a blue jumper or he wears a green jumper or he does not wear a jumper. The probability that he wears a blue jumper is 0.6 and the probability that he wears a green jumper is 0.3 . Whether Cooper wears a jumper of either colour, or does not wear a jumper, on any day is independent of his choice on any other day.

Use a suitable approximation to find the probability that, in any 150-day period, Cooper does not wear a jumper on fewer than 22 days.

Question 6

[Maximum number: 7]

The mass of grapes sold per day by a large shop can be modelled by a normal distribution with mean 28 kg . On 10 % of days less than 16 kg of grapes are sold.

Question 6(a)

(a)

Find the standard deviation of the mass of grapes sold per day.

[ 3 ]

Question 6(c)

(b)

In a random sample of 365 days, on how many days would you expect the mass of grapes sold to be within 1.3 standard deviations of the mean?

[ 4 ]

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 ]