Binomial from normal with unknown parameter

An unknown parameter (μ or σ) must first be found from given information before computing the normal probability to use in a binomial or repeated-trial calculation.

3 questions · Standard +0.3

Sort by: Default | Easiest first | Hardest first
CAIE S1 2017 November Q7
12 marks Standard +0.3
7 Josie aims to catch a bus which departs at a fixed time every day. Josie arrives at the bus stop \(T\) minutes before the bus departs, where \(T \sim \mathrm {~N} \left( 5.3,2.1 ^ { 2 } \right)\).
  1. Find the probability that Josie has to wait longer than 6 minutes at the bus stop.
    On \(5 \%\) of days Josie has to wait longer than \(x\) minutes at the bus stop.
  2. Find the value of \(x\).
  3. Find the probability that Josie waits longer than \(x\) minutes on fewer than 3 days in 10 days.
  4. Find the probability that Josie misses the bus.
Edexcel S1 2022 January Q5
11 marks Standard +0.3
  1. Jia writes a computer program that randomly generates values from a normal distribution. He sets the mean as 40 and the standard deviation as 2.4
    1. Find the probability that a particular value generated by the computer program is less than 37
    Jia changes the mean to \(m\) but leaves the standard deviation as 2.4
    The computer program then randomly generates 2 independent values from this normal distribution. The probability that both of these values are greater than 32 is 0.16
  2. Find the value of \(m\), giving your answer to 2 decimal places. Jia now changes the mean to 4 and the standard deviation to 8
    The computer program then randomly generates 5 independent values from this normal distribution.
  3. Find the probability that at least one of these values is negative.
Edexcel S2 2002 June Q5
13 marks Standard +0.3
A garden centre sells canes of nominal length 150 cm. The canes are bought from a supplier who uses a machine to cut canes of length \(L\) where \(L \sim \mathrm{N}(\mu, 0.3^2)\).
  1. Find the value of \(\mu\), to the nearest 0.1 cm, such that there is only a 5\% chance that a cane supplied to the garden centre will have length less than 150 cm. [4]
A customer buys 10 of these canes from the garden centre.
  1. Find the probability that at most 2 of the canes have length less than 150 cm. [3]
Another customer buys 500 canes.
  1. Using a suitable approximation, find the probability that fewer than 35 of the canes will have length less than 150 cm. [6]