Q1 Explain in detail what is meant by the term “random variable”. AC 1.1/1.2 Q2. A fair coin is…

Q1 Explain in detail what is meant by the term “random variable”. AC 1.1/1.2 Q2. A fair coin is…
  Q1 Explain in detail what is meant by the term “random variable”. AC 1.1/1.2 Q2. A fair coin is tossed 6 times and the random variable T represents the number of tails obtained (a) Give two reasons why a binomial model would be a suitable distribution for modelling T. a AC 1.1 (6) Find P(T = 5) AC 1.2 (c) Find the probability of obtaining more tails than heads. AC 1.2 A second coin is biased such that the probability of obtaining a head is This second coin is tossed 6 times. (d) Find the probability that, for the second coin, the number of heads obtained is greater than or equal to the number of tails obtained. AC 1.2 Q3. The heights, F cm, of an adult female population are normally distributed with mean 165 cm and standard deviation 7.4 cm. (a) Give two properties of the normal distribution which make it suitable for modelling this random variable. AC 2.1 (b) Find the probability that a randomly chosen adult female is taller than 152 cm. AC 2.2 Sarah is a young girl. She visits her doctor and is told that she is at the 58th percentile for height. (c) Assuming that Sarah remains at the 58th percentile, estimate her height as an adult. AC 2.2 The heights, Mcm, of an adult male population are normally distributed with standard deviation 9.0 cm. Given that 88% of adult males are taller than the mean height of adult females, (d) find the mean height of an adult male. AC 2.2 Q4. The time taken for a randomly selected person to complete a test is M minutes, where M-N(14,02) Given that 10% of people take less than 12 minutes to complete the test, (a) find the value of a AC 2.2 Graham selects 15 people at random. (b) Find the probability that fewer than 2 of these people will take less than 12 minutes to complete the test. AC 1.2 May 16 2022 05:48 PM

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