### Probability Analysis of a Gender-Selection TechniqueA gender-selection technique is designed to increase the likelihood that a baby will be a girl. In the results of the gender-selection technique, 856 births consisted of 438 baby girls and 418 baby boys. In analyzing these results, assume that boys and girls are equally likely.**Tasks and Analysis:**a. **Calculation of Probability for Exactly 438 Girls:** - Find the probability of getting exactly 438 girls in 856 births.b. **Calculation of Probability for 438 or More Girls:** - Find the probability of getting 438 or more girls in 856 births. If boys and girls are equally likely, is 438 girls in 856 births unusually high?c. **Determining Relevant Probability:** - Which probability is relevant for trying to determine whether the technique is effective: the result from part (a) or the result from part (b)?d. **Effectiveness Assessment:** - Based on the results, does it appear that the gender-selection technique is effective?**Solution Outline:**> a. **Exact Probability Calculation:**>> The probability of getting exactly 438 girls in 856 births is ______. > > (Round to four decimal places as needed.)To find these probabilities, you will typically use the binomial distribution as boys and girls are assumed to be equally likely (p = 0.5 for both genders).**Note on Statistical Analysis:**- **Binomial Distribution:** This is used when there are fixed numbers of independent trials, each having two possible outcomes (in this case: boy or girl). - Formula for the binomial probability: \( P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \) where - \( n \) = number of trials, - \( k \) = number of successful outcomes, - \( p \) = probability of success on a single trial. - **Cumulative Probability:** For part (b), cumulative probability helps in determining the likelihood of having 438 or more successes (girls) out of 856 trials (births).This educational outline will guide users through the statistical thinking required to assess the effectiveness of the gender-selection technique, with specific focus on understanding probability, binomial distribution, and hypothesis testing.

Given, n = 856 p = 438/856 = 0.512

A gender-selection technique is designed to increase the likelihood that a baby will be a girl. In the results of the gender-selection technique, 856 births consisted of 438 baby girls and 418 baby boys. In analyzing these results, assume that boys and girls are equally likely. a. Find the probability of getting exactly 438 girls in 856 births. b. Find the probability of getting 438 or more girls in 856 births. If boys and girls are equally likely, is 438 girls in 856 births unusually high? c. Which probability is relevant for trying to determine whether the technique is effective: the result from part (a) or the result from part (b)? d. Based on the results, does it appear that the gender-selection technique is effective? a. The probability of getting exactly 438 girls in 856 births is. (Round to four decimal places as needed.)

A gender-selection technique is designed to increase the likelihood that a baby will be a girl. In the results of the gender-selection technique, 856 births consisted of 438 baby girls and 418 baby boys. In analyzing these results, assume that boys and girls are equally likely. a. Find the probability of getting exactly 438 girls in 856 births. b. Find the probability of getting 438 or more girls in 856 births. If boys and girls are equally likely, is 438 girls in 856 births unusually high? c. Which probability is relevant for trying to determine whether the technique is effective: the result from part (a) or the result from part (b)? d. Based on the results, does it appear that the gender-selection technique is effective? a. The probability of getting exactly 438 girls in 856 births is. (Round to four decimal places as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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