Home › AP Statistics › Statistics › Discrete Random Variables › A fair six-sided die is tossed twice, and X coun…
A fair six-sided die is tossed twice, and X counts the number of the two faces that show an even number. Using the 36-outcome sample space, what are the mean μ and standard deviation σ of X?
Aμ = 1, σ ≈ 0.7071
Bμ = 1, σ ≈ 1.4142
Cμ = 0.5, σ ≈ 0.7071
Dμ = 2, σ ≈ 0.7071
Answer & Solution
Correct answer: A. μ = 1, σ ≈ 0.7071
1. With two dice, X = 0, 1, or 2 even faces, with P(x=0)=9/36, P(x=1)=18/36, P(x=2)=9/36.
2. μ = (0)(9/36) + (1)(18/36) + (2)(9/36) = 0 + 0.5 + 0.5 = 1.
3. Summing (x-μ)^2*P(x) across the three outcomes gives 18/36, and sqrt(18/36) ≈ 0.7071.
4. Option B doubles the correct standard deviation, and options C and D shift the mean, so neither matches this symmetric distribution.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.2 Mean or Expected Value and Standard Deviation_
Related questions
Mrs. Plum's cats wake her up an average of ten times per week, so X ~ P(10). What is P(x≤5The average number of children a Spanish woman has in her lifetime is 1.47, so X ~ P(1.47)Pierre, an amateur chef, drops an average of 1.5 pieces of egg shell into each cake he bakContinuing the IRS audit example with X ~ P(2), what is P(x≥3), the probability that at leThe chance of an IRS audit for a return over $25,000 is about 2% per year. For 100 such taA manufacturer finds 3% of its Christmas light bulbs defective. For a string of 100 lightsFor 200 days with a 1.02% chance of low seismic activity per day in Alaska, the binomial mText message users send or receive an average of 41.5 texts per day. Converted to an hourl