### Understanding Normal Distribution in the Context of Dutch Male HeightsMales in the Netherlands are the tallest, on average, in the world, with an average height of 183 centimeters (cm). Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and a standard deviation of 10.5 cm. To answer the following questions, you may need to use the appropriate appendix table that provides the probabilities related to the standard normal distribution.#### Questions:**(a)** What is the probability that a Dutch male is shorter than 176 cm? (Round your answer to four decimal places.)[Input Box]**(b)** What is the probability that a Dutch male is taller than 196 cm? (Round your answer to four decimal places.)[Input Box]**(c)** What is the probability that a Dutch male is between 174 and 192 cm? (Round your answer to four decimal places.)[Input Box]**(d)** Out of a random sample of 1,000 Dutch men, how many would we expect to be taller than 188 cm? (Round your answer to the nearest integer.)[Input Box]### Guidance for Calculations:To find the probabilities for questions (a), (b), and (c), you will need to:1. Convert the height values to z-scores using the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where $ X $ is the height, $ \mu $ is the mean, and $ \sigma $ is the standard deviation. 2. Use the z-scores to find probabilities from a standard normal distribution table or using statistical software.For question (d), once you have the probability, multiply it by 1,000 to find the expected number of men taller than 188 cm in the sample.

P(X<176)=Px-μσ<176-18310.5=P(z<-0.67)=0.2514 Therefore the probability is 0.2514

Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm).t Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm. (a) What is the probability that a Dutch male is shorter than 176 cm? (Round your answer to four decimal places.) (b) What is the probability that a Dutch male is taller than 196 cm? (Round your answer to four decimal places.) (c) What is the probability that a Dutch male between 174 and 192 cm? (Round your answer to four decimal places.) (d) Out of a random sample of 1,000 Dutch men, how many would we expect to be taller than 188 cm? (Round your answer to the nearest integer.) men

Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm).t Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm. (a) What is the probability that a Dutch male is shorter than 176 cm? (Round your answer to four decimal places.) (b) What is the probability that a Dutch male is taller than 196 cm? (Round your answer to four decimal places.) (c) What is the probability that a Dutch male between 174 and 192 cm? (Round your answer to four decimal places.) (d) Out of a random sample of 1,000 Dutch men, how many would we expect to be taller than 188 cm? (Round your answer to the nearest integer.) men

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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