Question

Let X equal the number of knots in each 100 meters of yarn. Assume that X has a Poisson distribution with mean 2.5. Let W equal the amount of meters before the first knot is found. (a) Give the mean number of knots per meter. (b) What is the probability distribution function of W ? (c) Give the mean and variance of W. (d) Find i. P(W <= 20) ii. P(W > 40) iii. P(W > 60|W > 20)

Name: let x equal the number of knots in each 100 meters of yarn assume that x has a poisson distribution with mean 25 let w equal the amount of meters before the first knot is found a give the me 89106
Uploaded: 2022-04-02T16:29:08-08:00
Duration: 1 min 50 s
Channel: Audrey Fong
Description: let x equal the number of knots in each 100 meters of yarn assume that x has a poisson distribution with mean 25 let w equal the amount of meters before the first knot is found a give the me 89106

          Let X equal the number of knots in each 100 meters of yarn. Assume that X has a Poisson distribution
with mean 2.5. Let W equal the amount of meters before the first knot is found.
(a) Give the mean number of knots per meter.
(b) What is the probability distribution function of W ?
(c) Give the mean and variance of W.
(d) Find
i. P(W <= 20)
ii. P(W > 40)
iii. P(W > 60|W > 20)

Added by Sandra G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Audrey Fong

04/02/2022

Step 1

Given that X has a Poisson distribution with a mean of 2.5 knots per 100 meters, we can find the mean number of knots per meter by dividing the given mean by 100: \[ \text{Mean per meter} = \frac{2.5}{100} = 0.025 \text{ knots per meter} \] Show more…

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Let X equal the number of knots in each 100 meters of yarn. Assume that X has a Poisson distribution with mean 2.5. Let W equal the amount of meters before the first knot is found. (a) Give the mean number of knots per meter. (b) What is the probability distribution function of W ? (c) Give the mean and variance of W. (d) Find i. P(W <= 20) ii. P(W > 40) iii. P(W > 60|W > 20)