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.

4 questions · Moderate -0.4

2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation
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CAIE S1 2013 June Q3
6 marks Moderate -0.8
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
9 marks Moderate -0.8
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.
Edexcel S1 2011 June Q2
5 marks Moderate -0.8
The random variable \(X \sim \text{N}(\mu, 5^2)\) and \(\text{P}(X < 23) = 0.9192\)
  1. Find the value of \(\mu\). [4]
  2. Write down the value of \(\text{P}(\mu < X < 23)\). [1]
OCR S2 2012 January Q3
6 marks Standard +0.8
The random variable \(G\) has a normal distribution. It is known that $$\text{P}(G < 56.2) = \text{P}(G > 63.8) = 0.1.$$ Find P(\(G > 65\)). [6]