Manufacturers don’t like defective products because it can give their brands a bad reputation. However, no production line is perfect. One line is filling soda bottles that are supposed to contain 2 liters. Typically, 99% of these bottles are properly filled. In a quality control sample of 25 bottles, what is the probability that at least 23 are properly filled?

0.99804932311

Step-by-step explanation:

We solve this using binomial probability

Binomial probability formula

= nCx × p^x × q^n - x

= n!/(n - x)! x!

Where n = Number of trials = 25 samples

x = Number of successes = 23

p = probability of success = 99% = 0.99

q = probability of failure = 1 - p

= 1 - 0.99

= 0.01

Hence,

p(at least 23 are properly filled) = p(X ≥ x)

= [25!/(25 - 23)! × 23! × 0.99^23 × 0.01^25 - 23 ]+ [25!/(25 - 24)! × 24! × 0.99^24 × 0.01^25 - 24 ]+ [25!/(25 - 25)! × 23! × 0.99^25 × 0.01^25 - 25]

= [300 × 0.99 ^23 × 0.01^2] + [25 × 0.99^24 × 0.01^1] + [1 × 0.99^25 + 0.01^0]

= 0.0238084285 + 0.1964195352 + 0.7778213594

= 0.99804932311

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

step-by-step explanation:

when the line is solid:

when the line is dashed:

this > inequality sign means:

this < inequality sign means:

this > inequality sign means:

this < inequality sign means:

about the problem:

srry i'm not done ! i'll