Question

According to a university research report, 58% of graduate students believe saving energy should be given priority for developed countries. Suppose that a professor randomly selects 18 students and ask their opinion.
a) What is the probability that exactly 14 students vote in favour of saving energy?
b) What is the probability that 6 students and more vote in favour of saving energy?
c) What is the probability that less than 9 students vote in favour of saving energy?

Answer 1

Answer:

Step-by-step explanation:

Probability of favour of saving energy = 0.58

Probability against = 1 - 0.58 = 0.42

Total Students = 18

Probability that exactly 14 students vote in favour of saving energy

= ¹⁸C₁₄(0.58)¹⁴(0.42)⁴

What is the probability that 6 students and more vote in favour of saving energy?

= 1  - ¹⁸C₀(0.58)⁰(0.42)¹⁸ - ¹⁸C₁(0.58)¹(0.42)¹⁷ - ¹⁸C₂(0.58)²(0.42)¹⁶ - ¹⁸C₃(0.58)³(0.42)¹⁵ - ¹⁸C₄(0.58)⁴(0.42)¹⁴ - ¹⁸C₅(0.58)⁵(0.42)¹³

probability that less than 9 students vote in favour of saving energy

¹⁸C₀(0.58)⁰(0.42)¹⁸ + ¹⁸C₁(0.58)¹(0.42)¹⁷ + ¹⁸C₂(0.58)²(0.42)¹⁶ + ¹⁸C₃(0.58)³(0.42)¹⁵ + ¹⁸C₄(0.58)⁴(0.42)¹⁴ + ¹⁸C₅(0.58)⁵(0.42)¹³  + ¹⁸C₆(0.58)⁶(0.42)¹²  + ¹⁸C₇(0.58)⁷(0.42)¹¹  + ¹⁸C₈(0.58)⁸(0.42)¹⁰