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%. For a random sample of 200 people, X ~ B(200, 0.0128) counts those who will develop it. What are the mean and standard deviation of X?
Aμ = 2.56, σ ≈ 2.56
Bμ = 2.56, σ ≈ 1.59
Cμ = 1.28, σ ≈ 1.59
Dμ = 200.0, σ ≈ 0.0128
Answer & Solution
Correct answer: B. μ = 2.56, σ ≈ 1.59
1. Apply μ = np: μ = (200)(0.0128) = 2.56.
2. Apply σ = sqrt(npq): σ = sqrt((200)(0.0128)(0.9872)) ≈ 1.5897, which rounds to 1.59.
3. So the expected count is 2.56 people with a standard deviation of about 1.59.
4. Option A repeats μ as if it were σ, and option D leaves n and p unmultiplied, so neither is correct.
_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