Question

A. When a person is selected at random from a very large population, the probability that the selected person has brown eyes is 0.62. If 4 people are selected at random, find the following probabilities :

1. they all have brown eyes

2. none of them have brown eyes

B. In a study of sandhill cranes, the distance traveled in one day is normally distributed, with a mean of 267 kilometers and a standard deviation of 86 km. Find the probability that the distance traveled in a day by a randomly selected crane is greater than 500 km.

Answer 1

(A) Probability that the person will have brown eyes = 0.62

Probability that the person will not have brown eyes = 1 - 0.62 = 0.38

(1) Probability that the all have brown eyes = ⁴C₄ (0.62)⁴ (0.38)^4-4

= 1 × 0.148 × 1

= 0.148 ~ 0.15​​​​​​

(2) Probability that none of them have brown eyes

= ⁴C₀ (0.62)⁰ (0.38)^4-0

= 1 × 1 × 0.02

= 0.02

(B) mean = 267 km

Standard deviation = 86 km

Let the distance travelled in a day = X

P(X=500) = 500 - 267/86 = 2.70

Z value for 2.70 = 0.9965

Probability that the distance travelled in a day is greater than 500km

P(x>500) = 1 - 0.9965 = 0.0035 or 0.35%