November 2025 (9709/52). Question 3

The heights of the 124 Senior members of the Giraffes basketball club are normally distributed with mean 187.4cm and standard deviation 6.4cm.

(a) How many members of the club would you expect to have heights within 5cm of the mean? [4 marks]

The heights of the Junior members of the Giraffes club are normally distributed with mean 172.7cm and standard deviation cm. 23% of these members have height less than 170.3cm.

(b) Find the value of [3 marks]

November 2025 (9709/52). Question 6

For a randomly chosen person, their next birthday is equally likely to occur on any day of the week, independently of any other person’s birthday.

(a) Find the probability that, out of 10 randomly chosen people, none of them will have their next birthday on a Saturday or Sunday. [1 mark]

(b) Find the probability that, out of 10 randomly chosen people, fewer than 3 will have their next birthday on a Wednesday. [3 marks]

9709/51/M/J/25q1 – Mark Scheme

The masses of the bags of rice made by a company are normally distributed with mean kg and standard deviation 0.14kg. The probability that the mass of a randomly chosen bag of this rice is less than 1.48kg is 0.22.

Find the value of [3 marks]

9709/51/M/J/25q4 – Mark Scheme

Every Saturday, a particular community holds a “Puzzle” event to raise money for a new Leisure Centre. Competitors attempt to solve a puzzle as quickly as possible.

Last Saturday, 600 competitors took part. The times taken to complete the puzzle were normally distributed with mean 32.4 minutes and standard deviation 2.5 minutes.

(a) How many competitors would you expect to have times within 1.2 minutes of the mean time. [4 marks]

In this Saturday’s event, 60% of the competitors had times less than 36.0 minutes.

(b) 9 competitors who took part in this Saturday’s event are selected at random.

Find the probability that at least 2 and fewer than 8 of these competitors had times less than 36.0 minutes. [3 marks]

(c) 80 competitors who took part in this Saturday’s event are selected at random.

Unse a suitable approximation to find the probability that more than 50 of these competitors had times less than 36.0 minutes. [5 marks]

9709/52/M/J/25q2 – Mark Scheme

In Millford, 70% of the residents own a bicycle. A random sample of 160 residents is selected.

Use a suitable approximation to find the probability that more than 120 of these residents own a bicycle. [5 marks]

9709/52/M/J/25q7 – Mark Scheme

Kestrels are birds whose adult wingspans are normally distributed with mean 74.8cm and standard deviation 3.2cm. A random sample of 120 adult kestrels is selected.

(a) How many of these 120 adult kestrels would you expect to have wingspan between 72.4cm and 76.3cm? [4 marks]

The masses of adult kestrels are normally distributed with mean kg and standard deviation kg. It is known that 20% of adult kestrels have mass greater than 0.202kg and 28% have mass less than 0.185kg.

(b) Find the value of and the value of . [5 marks]

10 adult kestrels are selected at random.

(c) Find the probability that fewer than 3 have masses greater than 0.202kg. [3 marks]

9709/53/M/J/25q6 – Mark Scheme

A company sells bags of pasta. The masses of large bags of pasta are normally distributed with mean 2.50 kg and standard deviation 0.12kg.

(a) Find the probability that the mass of pasta in a randomly chosen large bag is less than 2.65kg. [2 marks]

A restaurant manager buys 160 of these large bags of pasta.

(b) Find the number of bags for which you would expect the mass of pasta to be more than 1.65 standard deviations above the mean. [3 marks]

The masses of small bags of pasta sold by the company are normally distributed with mean kg and standard deviation kg. Tests show that 77% of these bags have masses greater than 1.26kg, and 44% have masses less than 1.35kg.

(c) Find, in either order, the value of and the value of . [5 marks]