Home › AP Statistics › Statistics › Discrete Random Variables › The lifetime risk of pancreatic cancer is about …
The lifetime risk of pancreatic cancer is about 1.28%. Let X ~ G(0.0128) count how many people you must ask until one says they have it. What are the mean and standard deviation of X?
Aμ ≈ 78, σ ≈ 77.62
Bμ ≈ 78, σ ≈ 1.28
Cμ ≈ 1.28, σ ≈ 77.62
Dμ ≈ 128, σ ≈ 77.62
Answer & Solution
Correct answer: A. μ ≈ 78, σ ≈ 77.62
1. μ = 1/p = 1/0.0128 ≈ 78.13, which rounds to about 78 people.
2. σ = sqrt((1/p)(1/p - 1)) = sqrt((78.125)(77.125)) ≈ 77.62.
3. So on average you would need to ask about 78 people, with a standard deviation near 77.62.
4. Option D misreads 1.28% as 128 rather than 0.0128, giving the wrong mean entirely.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.4 Geometric 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