in a particular university the probability that any one student is male is 0.65 . four students are selected at random from the University as a sample. (a) create probability distribution of the sample proportion of female students in the sample/(4dp). (b) find pr (p hat is greater than 0.65/ phat is greater than 0).
Answers
Given : the probability that any one student is male is 0.65 . four students are selected at random from the University as a sample
To Find : probability distribution of the sample proportion of female students in the sample
Solution:
Probability of any student male p = 0.65
Probability of any student female q = 1 - p = 1-0.65 = 0.35
For female students
p = 0.35 , q = 0.65 n = 4
P(x) = ⁿCₓpˣqⁿ⁻ˣ
P(0) = ⁴C₀(0.35)⁰(0.65)⁴ = 0.1785
P(1) = ⁴C₁(0.35)¹(0.65)³ = 0.3845
P(2) = ⁴C₂(0.35)²(0.65)² = 0.3105
P(3) = ⁴C₃(0.35)³(0.65)¹ = 0.1115
P(4) = ⁴C₄(0.35)⁴(0.65)⁰ = 0.0150
∑ x(P(x)
0.1785 * 0 + 0.3845*1 + 0.3105 * 2 + 0.1115* 3 + 0.0150* 4
= 0 + 0.3845 + 0.621 + 0.3345 + 0.06
= 1.4
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