Find k given probability statement

Given a normal distribution with known mean and standard deviation, find the unknown value k from a probability statement like P(X < k) = p or P(X > k) = p.

4 questions

CAIE S1 2016 November Q1
1 The random variable \(X\) is such that \(X \sim \mathrm {~N} ( 20,49 )\). Given that \(\mathrm { P } ( X > k ) = 0.25\), find the value of \(k\).
Edexcel S1 2015 January Q7
  1. The birth weights, \(W\) grams, of a particular breed of kitten are assumed to be normally distributed with mean 99 g and standard deviation 3.6 g
    1. Find \(\mathrm { P } ( W > 92 )\)
    2. Find, to one decimal place, the value of \(k\) such that \(\mathrm { P } ( W < k ) = 3 \mathrm { P } ( W > k )\)
    3. Write down the name given to the value of \(k\).
    For a different breed of kitten, the birth weights are assumed to be normally distributed with mean 120 g Given that the 20th percentile for this breed of kitten is 116 g
  2. find the standard deviation of the birth weight of this breed of kitten.
OCR S2 2011 June Q2
2 The random variable \(Y\) has the distribution \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\). It is given that $$\mathrm { P } ( Y < 48.0 ) = \mathrm { P } ( Y > 57.0 ) = 0.0668 .$$ Find the value \(y _ { 0 }\) such that \(\mathrm { P } \left( Y > y _ { 0 } \right) = 0.05\).
Edexcel S1 2003 June Q2
2. The lifetimes of batteries used for a computer game have a mean of 12 hours and a standard deviation of 3 hours. Battery lifetimes may be assumed to be normally distributed. Find the lifetime, \(t\) hours, of a battery such that 1 battery in 5 will have a lifetime longer than \(t\).