Home › AP Statistics › Statistics › Discrete Random Variables › For pancreatic cancer risk X ~ B(200, 0.0128), a…
For pancreatic cancer risk X ~ B(200, 0.0128), a binomial calculator gives P(x=5) = 0.0707 and P(x=6) = 0.0298. Which is more likely, that exactly five people or exactly six people develop the cancer in this sample?
ASix people, since P(x=6) exceeds P(x=5)
BThey are equally likely outcomes
CFive people, since P(x=5) exceeds P(x=6)
DNeither, since both probabilities round to zero
Answer & Solution
Correct answer: C. Five people, since P(x=5) exceeds P(x=6)
1. Compare the two given binomial probabilities directly: P(x=5) = 0.0707 versus P(x=6) = 0.0298.
2. 0.0707 is larger than 0.0298.
3. So five is the more likely count of people developing pancreatic cancer in this sample.
4. Option D is false because neither probability actually rounds to zero, and option C ignores that the two values differ.
_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