1) The probability that an individual is left-handed is 12%. In a randomly selected class of 30 students, what is the probability of finding exactly 4 left-handed students? 2) Sixty-five percent of men consider themselves knowledgeable football fans. If 10 men are randomly selected, find the probability that exactly six of them will consider themselves knowledgeable fans.

0.2047

0.2377

Step-by-step explanation:

1.

What we have here is a binomial distribution

Probability p = 0.12

N = number of students in the class = 30

Probability of finding 4 left handers

P(x = 4) = 30C4 x (0.12)⁴ x (0.88)²⁶

= 27405 x 0.00020736 x 0.03602047835

= 0.2047

2.

This is also a binomial distribution

N = 10 p = 0.65

P(of 6 knowledgeable fans)

= 10C6 x (0.65)⁶ x (0.35)⁴

= 210 x 0.0754189 x 0.01500625

= 0.2377

38.6°

step-by-step explanation:

resultant is 10 pound

smaller force = 8 pound

angle formed = tan⁻¹(

                        =tan⁻¹(

                          =tan⁻¹(0.8)

                        =38.6°