Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Question C : Assume each newborn baby has a probability of approximately 0.54 of

ID: 3072091 • Letter: Q

Question

Question C :

Assume each newborn baby has a probability of approximately 0.54 of being female and 0.46 of being male. For a family with three children, let X- number of children who are girls. a. Identify the three conditions that must be satisfied for X to have the binomial distribution. b. Identify n and p for the binomial distribution. c. Find the probability that the family has one girl and two boys a. Which of the below are the three conditions for a binomial distribution? I. The n trials are independent. IlI. The n trials are dependent. V. There are two trials. II. Each trial has at least two possible outcomes. IV. Each trial has the same probability of a success. VI. Each trial has two possible outcomes OA II, III, and V O B. III, V, and VI C. I, II, and IV D. I, IV, and VI b.n 3 p.54 c. The probability that the family has one girl and two boys is (Round to four decimal places as needed.)

Explanation / Answer

Given that, X = number of children who are girls.

Here, X ~ Binomial ( n = 3, p = 0.54)

Probability mass function of X is,

P(X = x) = nCx px (1-p)n-x

We want to find, P(X = 1)

P(X = 1)

= 3C1 * (0.54)1 * (1 - 0.54)3-1

= 3 * (0.54) * (0.46)2

= 3 * 0.54 * 0.2116

= 0.342792

= 0.3428

P(X = 1) = 0.3428

The probability that the family has one girl and two boys is 0.3428