**Finding the Probability Using Normal Approximation**To find the probability of the indicated number of voters, we will use a normal approximation. In this case, assume that 163 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.**Problem Statement:**Find the probability that fewer than 42 voters voted.**Given Data:**- Total eligible voters (n): 163- Proportion of voters (p): 22% (or 0.22)**Required Probability:**The probability that fewer than 42 of 163 eligible voters voted.**Solution Outline:**1. Calculate the mean (μ) and standard deviation (σ) of the binomial distribution. Formula for mean (μ): \[ \mu = np \] Formula for standard deviation (σ): \[ \sigma = \sqrt{np(1-p)} \] 2. Convert the binomial probability to a normal probability by using the normal approximation to the binomial distribution.3. Find the z-score for 42 voters.4. Use the z-score to find the corresponding probability from the standard normal distribution table.**Note:**- Remember to round your final answer to four decimal places as needed.---**Note to the students:**This example illustrates how to use the normal approximation to compute probabilities for a binomial distribution, especially when dealing with large sample sizes.For further explanation and detailed step-by-step solutions, refer to the section on "Normal Approximation to the Binomial Distribution" in your statistics textbook.(End of transcription)

Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 163 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted. Probability that fewer than 42 voted The probability that fewer than 42 of 163 eligible voters voted is (Round to four decimal places as needed.)

Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 163 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted. Probability that fewer than 42 voted The probability that fewer than 42 of 163 eligible voters voted is (Round to four decimal places as needed.)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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