Combined binomial and normal events

Calculate probabilities involving both exact binomial calculations for small samples and normal approximations for large samples in the same question.

30 questions

Edexcel S2 Q5
  1. Lupin seeds are sold in packets of 15 . On average, 9 seeds in a packet are green and 6 are red. Find, to 2 decimal places, the probability that in any particular packet there are
    1. less than 2 red seeds,
    2. more red than green seeds.
    The seeds from 10 packets are then combined together.
  2. Use a suitable approximation to find the probability that the total number of green seeds is more than 100 .
Edexcel S2 Q5
5. In a certain school, \(32 \%\) of Year 9 pupils are left-handed. A random sample of 10 Year 9 pupils is chosen.
  1. Find the probability that none are left-handed.
  2. Find the probability that at least two are left-handed.
  3. Use a suitable approximation to find the probability of getting more than 5 but less than 15 left-handed pupils in a group of 35 randomly selected Year 9 pupils.
    Explain what adjustment is necessary when using this approximation. \section*{STATISTICS 2 (A) TEST PAPER 3 Page 2}
Edexcel S2 Q6
6. In a particular parliamentary constituency, the percentage of Conservative voters at the last election was \(35 \%\), and the percentage who voted for the Monster Raving Loony party was \(2 \%\).
  1. Find the probability that a random sample of 10 electors includes at least two Conservative voters. Use suitable approximations to find
  2. the probability that a random sample of 500 electors will include at least 200 who voted either Conservative or Monster Raving Loony,
  3. the probability that a random sample of 200 electors will have at least 5 Monster Raving Loony voters in it.
  4. One of (b) or (c) requires an adjustment to be made before a calculation is done. Explain what this adjustment is, and why it is necessary.
Edexcel S2 Q3
3. The sales staff at an insurance company make house calls to prospective clients. Past records show that \(30 \%\) of the people visited will take out a new policy with the company. On a particular day, one salesperson visits 8 people. Find the probability that, of these,
  1. exactly 2 take out new policies,
  2. more than 4 take out new policies. The company awards a bonus to any salesperson who sells more than 50 policies in a month.
  3. Using a suitable approximation, find the probability that a salesperson gets a bonus in a month in which he visits 150 prospective clients.
    (5 marks)
SPS SPS SM Statistics 2022 February Q13
13. Sam is playing a computer game. When Sam earns a reward in the game, she randomly receives either a Silver reward or a Gold reward. Each time that Sam earns a reward, the probability of receiving a Gold reward is 0.4 One day Sam plays the computer game and earns 11 rewards.
  1. Find the probability that she receives
    1. exactly 2 Gold rewards,
    2. at least 5 Gold rewards. In the next month Sam earns 300 rewards.
      She decides to use a Normal distribution to estimate the probability that she will receive at least 135 Gold rewards.
    1. Find the mean and variance of this Normal distribution.
    2. Estimate the probability that Sam will receive at least 135 Gold rewards.
      [0pt] [BLANK PAGE]