A factory bought a new machine. It is not configured well yet, so the probability of defects is 0.05. Estimate the probability that there are at most 2 spoiled details in the random sample of 20.

Pr(at most 2 are defective) = 0.38

Step-by-step explanation:

probability of defective = 0.05

probability of not  defective =1- 0.05 = 0.95

Pr(at most 2 are defective) = pr (0 defective) +  pr (1 defective) + pr (2defective)

pr (0 defective) = (0.05^0) * (0.95^20) = 0.36

pr (1 defective) =  (0.05^1) * (0.95^19) = 0.019

pr (2 defective) =  (0.05^2) * (0.95^18) = 0.0025 * 0.397 = 0.00099

Pr(at most 2 are defective) =  0.36 +  0.019 +  0.00099

Pr(at most 2 are defective) = 0.37999 = 0.38

a and c

step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.