Home › AP Statistics › Statistics › Discrete Random Variables › About 41% of adult workers have a high school di…
About 41% of adult workers have a high school diploma but pursue no further education. For a random sample of 20 such workers, X ~ B(20, 0.41). What are the mean and standard deviation of X?
Aμ = 8.2, σ ≈ 4.84
Bμ = 20.0, σ ≈ 0.41
Cμ = 4.1, σ ≈ 2.20
Dμ = 8.2, σ ≈ 2.20
Answer & Solution
Correct answer: D. μ = 8.2, σ ≈ 2.20
1. For a binomial variable, μ = np and σ = sqrt(npq).
2. μ = (20)(0.41) = 8.2, the expected number of such workers.
3. σ = sqrt((20)(0.41)(0.59)) = sqrt(4.838) ≈ 2.20.
4. Option A squares the standard deviation by mistake, and options C and D swap or misapply n, p, and q.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.3 Binomial Distribution_
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