Simplify the expression show steps
1 answer:
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Answer:
a) 0.0287 = 2.87% probability that three non-defective components in a batch of seven components.
b) 0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.
Step-by-step explanation:
A sequence of Bernoulli trials composes the binomial distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
The probability that a selected component is non-defective is 0.8
This means that
a) Three non-defective components in a batch of seven components.
This is P(X = 3) when n = 7. So
0.0287 = 2.87% probability that three non-defective components in a batch of seven components.
b) 8 non-defective components are drawn before the first defective component is chosen.
Now the order is important, so the we just multiply the probabilities.
8 non-defective, each with probability 0.8, and then a defective, with probability 0.2. So
0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.
Answer:
82.5 ft²
Step-by-step explanation:
The area (A) of a trapezoid is calculated as
A = h (b₁ + b₂)
where h is the perpendicular height and b₁, b₂ the parallel bases
Here h = 7.5, b₁ = 7 and b₂ = 15 , then
A = × 7.5 × (7 + 15) = 0.5 × 7.5 × 22 = 82.5 ft²