QCEVault

Continuous random variables and the normal distribution — Question 373

Original QCE Vault practice · 5 marks

Q373 · Practice questionTechnology-activeComplex familiar5 marks

QUESTION 373 (5 marks)

Test scores are normally distributed. The 20th percentile is 8282 and the 80th percentile is 9898.
a)
Determine the mean and standard deviation, giving the standard deviation to three decimal places.
[3 marks]
b)
Determine the probability of a score above 110110, to four decimal places.
[2 marks]
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