Symmetric probability given

One probability statement involves a symmetric interval around the mean (e.g., P(μ - 2k < X < μ + 2k) = 0.6) or explicitly states P(X < μ) = 0.5, simplifying one equation.

2 questions

CAIE S1 2013 June Q3
3 Cans of lemon juice are supposed to contain 440 ml of juice. It is found that the actual volume of juice in a can is normally distributed with mean 445 ml and standard deviation 3.6 ml .
  1. Find the probability that a randomly chosen can contains less than 440 ml of juice. It is found that \(94 \%\) of the cans contain between \(( 445 - c ) \mathrm { ml }\) and \(( 445 + c ) \mathrm { ml }\) of juice.
  2. Find the value of \(c\).
Edexcel S1 2008 January Q6
6. The weights of bags of popcorn are normally distributed with mean of 200 g and \(60 \%\) of all bags weighing between 190 g and 210 g .
  1. Write down the median weight of the bags of popcorn.
  2. Find the standard deviation of the weights of the bags of popcorn. A shopkeeper finds that customers will complain if their bag of popcorn weighs less than 180 g .
  3. Find the probability that a customer will complain.