Problem 7-22 A food-packaging apparatus underfills 20% of the containers. Find the probability that for any particular 10 containers the number of underfilled will be: Note: This question uses a tolerance of .0001 for grading. Make sure your answers are entered to the fifth decimal place. Example: .00123

(a) exactly 2

P(X=2) = 0.30199

(b) exactly 4

P(X=4) = 0.08808

(c) exactly 10

P(X=10) ≈ 0.00000

(d) at least 5

P(X ≥ 5) = 0.03279

Step-by-step explanation:

This is a binomial distribution problem

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = number of containers to be considered = 10

x = Number of successes required = number of underfilled containers required

p = probability of success = probability that a container is underfilled = 0.20

q = probability of failure = probability that a container is NOT underfilled = 1 - 0.20 = 0.80

a) x = 2

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

P(X = 2) = ¹⁰C₂ (0.2)² (0.8)¹⁰⁻² = 0.30199

b) x = 4

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

P(X = 4) = ¹⁰C₄ (0.2)⁴ (0.8)¹⁰⁻⁴ = 0.08808

c) x = 10

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

P(X = 2) = ¹⁰C₁₀ (0.2)¹⁰ (0.8)¹⁰⁻¹⁰ ≈ 0.00000

d) x ≥ 5

P(X ≥ 5) = P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10)

Solving for each of these probabilities and summing them all up,

P(X ≥ 5) = P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10) = 0.0327934976 = 0.03279

Hope this Helps!!!

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

it's