**Understanding Normal Distribution in Pregnancy Durations**The lengths of pregnancies in a small rural village are normally distributed with a mean of 263 days and a standard deviation of 14 days. A distribution of values is normal with a mean of 263 and a standard deviation of 14.**Question:**What percentage of pregnancies last beyond 305 days?\[ P(X > 305 \text{ days}) = \_\_\_\_ \% \]**Instructions:**- Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign).- Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.**Answer Submission:**- Click the "Submit Question" button to record your answer.**Need Help?**- Click "Message instructor" for assistance with this question.This exercise helps reinforce concepts in statistics, particularly how to apply z-scores and the properties of the normal distribution to real-world scenarios.

Answered: The lengths of pregnancies in a small…

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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Find SAT Quartiles. SAT scores are reported on a scale from 600 to 2400. The mean is 1498 and the standard deviation is 316. The quartiles of any distribution are the values with cumulative proportions 0.25, and 0.75. What are the quartiles of the distribution of SAT scores?
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that an individual has an IQ higher than 94. Find the probability that an individual has an IQ between 85 and 112. Find the IQ score that separates the highest scoring 28.1% from the rest of the population.
A distribution of values is normal with a mean of 190 and a standard deviation of 4.Find the interval containing the middle-most 30% of scores: Enter your answer using interval notation. Example: (2.1,5.6)
Jse the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 64 miles per hour, with a standard deviation of 4 miles per hour. Estimate the percent of vehicles whose speeds are between miles per hour and 72 miles per hour. (Assume the data set has a bell-shaped distribution.) Approximately % of vehicles travel between 56 miles per hour and 72 miles per hour.
A distribution of values is normal with a mean of 120 and a standard deviation of 4.Find the interval containing the middle-most 68% of scores: Enter your answer using interval notation. Example: (2.1,5.6)
As an electrical engineer, you have designed a new efficient light bulb. In order to predict its life expectancy, you conducted a series of experiments on 135 of these light bulbs and gathered the data shown in the table. Plot the data and calculate the mean and standard deviation.
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the minimum IQ required to be able to correctly claim to be in the "top 5%" of IQ scores. Round to the nearest whole number.
IQ scores of people around the world are normally distributed, with a mean of 100 and a standard deviation of 15. A genius is someone with an IQ greater than or equal to 145. What percent of the population is considered a genius? answer as a percent rounded to 2 decimal places
Lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 13 days. A baby is considered premature if the pregnancy length is at or below the third percentile (P3) of all pregnancy lengths. Find the length of pregnancy in days that separates the premature babies from those that are not considered premature. Round to the nearest integer.
answer D,E,F
z Scores LeBron James, one of the most successful basketball players of all time, has a height of 6 feet 8 inches, or 203 cm. Based on statistics from Data Set 1 “Body Data” in Appendix B, his height converts to the z score of 4.07. How many standard deviations is his height above the mean?
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 8.4 years, and standard deviation of 2.7 years. The 7% of items with the shortest lifespan will last less than how many years? Give your answer to one decimal place. years

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