Home › AP Statistics › Statistics › Discrete Random Variables › Pierre, an amateur chef, drops an average of 1.5…
Pierre, an amateur chef, drops an average of 1.5 pieces of egg shell into each cake he bakes, so X ~ P(1.5). If you buy one of his cakes each week for six weeks, what is the probability that NONE of the six cakes contain any egg shell?
AAbout 0.2231
BAbout 1.3386
CAbout 0.7769
DAbout 0.0001
Answer & Solution
Correct answer: D. About 0.0001
1. For one cake, P(x=0) = e^-1.5 ≈ 0.2231.
2. The six weekly cakes are independent, so the chance all six have zero egg shell is (0.2231)^6.
3. (0.2231)^6 ≈ 0.0001.
4. Option A is the probability for a single cake, not all six, and option C exceeds one, which is impossible for a probability.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.6 Poisson 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)Continuing 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 hourlAn email user receives 147 emails per day on average, so X ~ P(147). What is the standard