Statistics practice exam with answers

A full practice exam covering measures of location and spread, counting, binomial, Poisson and normal distribution, confidence intervals, tests and regression. Answer online and get it checked at once, or print it with or without worked answers. New exams with different numbers come with a free account.

8 questions · 42 points · about 60 minutes

1. Question 1

   6 points

   Task

   Work out Pearson's correlation coefficient for these pairs.

   x	y
   1	11
   2	14
   3	15
   6	20
   7	21

   r (2 decimal places)

   Comma or point; fractions like 1/6 work too.

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2. Question 2

   4 points

   Task

   In a contest with 9 teams, places 1 to 3 are awarded. How many different results are possible?

   Number

   Comma or point; fractions like 1/6 work too.

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3. Question 3

   4 points

   Task

   The random variable X has this distribution. Work out the expected value and the variance.

   x	P(X = x)
   0	0.25
   2	0.25
   3	0.25
   5	0.25

   E(X) (2 decimal places)

   Var(X) (2 decimal places)

   Comma or point; fractions like 1/6 work too.

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4. Question 4

   6 points

   Task

   Two-way table: passed (P) and attended lectures (A). What is P(P | A)?

   	A	not A
   P	25	48
   not P	13	34

   P (4 decimal places)

   Comma or point; fractions like 1/6 work too.

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5. Question 5

   6 points

   Task

   The fill volume is normal with μ = 50 ml and σ = 10 ml. Which volume do 99.0% of packs fall below? (z = 2.326)

   x (2 decimal places)

   Comma or point; fractions like 1/6 work too.

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6. Question 6

   6 points

   Task

   A maker claims μ = 100. A sample of n = 25 gives x̄ = 102.64; σ = 8 is known. Test H₀: μ = 100 two-sided at α = 5% (critical value 1.96).

   Test statistic z (2 decimal places)

   Decision

   Reject H₀Do not reject H₀

   Comma or point; fractions like 1/6 work too.

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7. Question 7

   6 points

   Task

   A sample of n = 36 has mean x̄ = 54.6; σ = 12 is known. Find the 99% confidence interval for μ (z = 2.576).

   Lower limit (2 decimal places)

   Upper limit (2 decimal places)

   Comma or point; fractions like 1/6 work too.

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8. Question 8

   4 points

   Task

   8 parts are checked; each is faulty with probability 0.10. What is P(at most 2 faulty)?

   P(X ≤ 2) (4 decimal places)

   Comma or point; fractions like 1/6 work too.

   Check Hint

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