Petrol consumption for all small cars is normally distributed with µ=30.5m.p.g and σ=4.5 m.p.g. a manufacturer wants to make a car that is more economical than 95% of small cars. What must be its m.p.g. Use a computer.

Question Three

a)      Petrol consumption for all small cars is normally distributed with µ=30.5m.p.g and σ=4.5 m.p.g. a manufacturer wants to make a car that is more economical than 95% of small cars. What must be its m.p.g. Use a computer.

b)      In a study of efficiency of a lie-detector test, 1000 people were given the test. Of these 500 lied and 500 told the truth. The lie-detector said that 185 of those who were telling the truth were liars and that 120 of the liars told the truth. Consider a single person who is about to take a lie-detector test.

Required:

i)                    Write down the null and alternative hypotheses for such a test

ii)                  Suppose the lie-detector says that he is lying. Is this evidence that you should reject the null hypothesis or not?

iii)                Is the lie-detector test a good one or not?