QCEVault

Continuous random variables and the normal distribution — Question 93

Original QCE Vault practice · 5 marks

Q93 · Practice questionTechnology-activeComplex unfamiliar5 marks

QUESTION 93 (5 marks)

The lifetime XX of a component is normally distributed with mean 120120 hours and standard deviation 1818 hours. A component is classified as long-life if it is in the top 5% of lifetimes. Determine the long-life cutoff, and then determine P(X>150∣X is long-life)P(X>150\mid X\text{ is long-life}).
Question linkSyllabus coverage

Related questions

  1. Q8 · Original practice · 1 mark
    A continuous random variable has density f(x)=2xf(x)=2x for 0≤x≤10\le x\le1. Determine P(X>0.6)P(X>0.6).
    Continuous random variables and the normal distribution
  2. Q18 · Original practice · 1 mark
    The random variable XX is normally distributed with mean 80 and standard deviation 5. Determine P(X<85)P(X<85).
    Continuous random variables and the normal distribution
  3. Q33 · Original practice · 2 marks
    A normally distributed variable XX has mean 60 and standard deviation 8. Determine P(X≤68)P(X\le68) to four decimal places.
    Continuous random variables and the normal distribution
  4. Q43 · Original practice · 5 marks
    A normally distributed random variable XX satisfies P(X<42)=0.10P(X<42)=0.10 and P(X<58)=0.90P(X<58)=0.90. Determine the mean and standard deviation of XX to three significant figures.
    Continuous random variables and the normal distribution