Question

Question 5 (2 points) A delivery of 877 motors comes with a problem. 41 of these were made with a defective connector. In a sample of 29, what is the probability of getting three or more with the defective parts?

Answer 1

The probability that a randomly selected motor was made with a defective connector

41 ដ 0.04675 877

Let X denotes the number of motors with defective parts in a random sample of 29 motors.

Here,

X ~ Binomial(n = 29, p = $\frac{41}{877}$ )

The probability mass function of X is

29 P(X = x) = 41 877' ** (1 41 29-1 *, x = 0,1,2, ..., 29 877'

Now,

The probability of getting three or more with the defective parts

$= P(X \geq 3)$

$= 1 - P(X\leq 2)$

$= 1 - \sum_{x=0}^{2} \binom{29}{x}*(\frac{41}{877})^x*(1 - \frac{41}{877})^{29-x}$

$\approx 0.1521$