SPS SPS SM Statistics 2026 January — Question 4 10 marks

Exam BoardSPS
ModuleSPS SM Statistics (SPS SM Statistics)
Year2026
SessionJanuary
Marks10
TopicBinomial Distribution
TypeBasic E(X) and Var(X) calculation
DifficultyEasy -1.2 This is a straightforward binomial distribution question requiring only direct application of standard formulas: E(X)=np, Var(X)=np(1-p), and basic probability calculations. All parts are routine textbook exercises with no problem-solving insight needed—students simply substitute values into memorized formulas and use calculator functions for binomial probabilities.
Spec2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities2.04d Normal approximation to binomial
4. Patrick is practising his skateboarding skills. On each day, he has 30 attempts at performing a difficult trick. Every time he attempts the trick, there is a probability of 0.2 that he will fall off his skateboard.
Assume that the number of times he falls off on any given day may be modelled by a binomial distribution.
    1. Find the mean number of times he falls off in a day.
      1. (ii) Find the variance of the number of times he falls off in a day.
      1. Find the probability that, on a particular day, he falls off exactly 10 times.
    3. (ii) Find the probability that, on a particular day, he falls off 5 or more times.
    4. Patrick has 30 attempts to perform the trick on each of 5 consecutive days.
      1. Calculate the probability that he will fall off his skateboard at least 5 times on each of the 5 days.
    6. (ii) Explain why it may be unrealistic to use the same value of 0.2 for the probability of falling off for all 5 days.
4.

Patrick is practising his skateboarding skills. On each day, he has 30 attempts at performing a difficult trick.

Every time he attempts the trick, there is a probability of 0.2 that he will fall off his skateboard.\\
Assume that the number of times he falls off on any given day may be modelled by a binomial distribution.
\begin{enumerate}[label=(\alph*)]
\item (i) Find the mean number of times he falls off in a day.\\
(a) (ii) Find the variance of the number of times he falls off in a day.
\item (i) Find the probability that, on a particular day, he falls off exactly 10 times.\\
(b) (ii) Find the probability that, on a particular day, he falls off 5 or more times.
\item Patrick has 30 attempts to perform the trick on each of 5 consecutive days.\\
(c) (i) Calculate the probability that he will fall off his skateboard at least 5 times on each of the 5 days.\\
(c) (ii) Explain why it may be unrealistic to use the same value of 0.2 for the probability of falling off for all 5 days.
\end{enumerate}

\hfill \mbox{\textit{SPS SPS SM Statistics 2026 Q4 [10]}}
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