Home › AP Statistics › Statistics › Discrete Random Variables › A student randomly guesses on a 32-question mult…
A student randomly guesses on a 32-question multiple-choice exam where each question has three choices, so X ~ B(32, 1/3). Passing with more than 75% correct means getting more than 24 questions right. What does the calculator find for P(x>24)?
AIt is close to one, near certainty of guessing that well
BIt equals exactly 0.75, matching the passing threshold
CIt equals exactly one third, matching the guessing rate
DIt is very small, essentially zero for random guessing
Answer & Solution
Correct answer: D. It is very small, essentially zero for random guessing
1. Under random guessing, X ~ B(32, 1/3), so the expected number correct is only about 32/3 ≈ 10.7.
2. Getting more than 24 correct out of 32 by pure guessing is far above that expected count.
3. A binomial calculator confirms P(x>24) is extremely small, practically zero.
4. Options A, B, and D each assign the wrong scale to this rare-event probability.
_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