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!!!

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

x= cost per bracelet

number of bracelets * x + shipping charge = total cost

so

9x+9=72