Question

g A random sample of 36 pairs of jeans is selected. Find the probability that less than 20% of them are defective. (Round your answer to 2 digits after the decimal point). A. 0.24 B. 0.41 C. 0.76 D. None of the above

Answer 1

Answer:

0.1684

Step-by-step explanation:

The whole question is attached.

This is a binomial probability question. The formula is:

$p(x)=\frac{n!}{(n-x)!x!}p^xq^{n-x}$

Where

n is the number in sample (here 36)

p is the probability of "success" (defective means "success", 25% = 0.25)

q is probability of failure (which is 1 - p = 1 - 0.25, q = 0.75)

Now,

we want probability defective LESS THAN 20%, it means:

36* 20% = 7.2

Basically, we want:

P(x < 7.2)

P(x < 7)

Which means P(x < 7) = P(x=0) + P(x=1) + P(x=2) + ..... + P(x=6)

Using cumulative distribution calculator, it will be:

P(x < 7) = 0.1684