Mathematics: A manufacturer of televisions subjects the equipment to a comprehensive testing process for all essential functions before the television leaves the factory. If the probability of passing these comprehensive tests is .95 and if 10 televisions are randomly selected what is that probability that at least 9 pass the test

A manufacturer of televisions subjects the equipment

potatogirl6811

07.02.2022

The probability is $P(X \le 9) =0.9138$

Step-by-step explanation:

From the question we are told that

The probability of the television passing the test is p = 0.95

The sample size is n = 10

Generally the comprehensive testing process for all essential functions follows a binomial distribution

i.e

$X \~ \ \ \ B(n , p)$

and the probability distribution function for binomial distribution is

$P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}$

Here C stands for combination hence we are going to be making use of the combination function in our calculators

Generally the probability that at least 9 pass the test is mathematically represented as

$P(X \le 9) = P(X = 9) + P(X = 10 )$

=> $P(X \le 9) = [^{10}C_9 * (0.95)^9 * (1- 0.95)^{10-9}]+ [^{10}C_{10} * {0.95}^{10} * (1- 0.95)^{10-10}]$

=> $P(X \le 9) = [10 * 0.6302 * 0.05 ]+ [1 *0.5987 * 1 ]$

=> $P(X \le 9) =0.9138$

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webbhlharryteach

09.11.2021

the length is approximately 13

Step-by-step explanation:

If a triangle has a hypotenuse, this means that it is right triangle. Knowing that it is right triangle we can use the Pythagorean Theorem

Pythagorean Theorem:

${a}^{2} + {b}^{2} = {c}^{2}$

${11}^{2} + {b}^{2} = {17}^{2}$

$121 + {b}^{2} = 289$

${b}^{2} = 289 - 121$

${b}^{2} = 168$

$b = \sqrt{168}$

b = 12.9614813968

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