Suppose the age that children learn to walk is normallydistributed with mean 11 months and standard deviation 1.2month. 18 randomly selected people were asked what agethey learned to walk. Round all answers to 4 decimal placeswhere possible.a. What is the distribution of X? X - N(|b. What is the distribution of æ? ¤ ~ N(c. What is the probability that one randomly selectedperson learned to walk when the person was between10 and 12 months old?d. For the 18 people, find the probability that theaverage age that they learned to walk is between 10and 12 months old.e. For part d), is the assumption that the distribution isnormal necessary? O NoO Yes

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Answered: Suppose the age that children learn to…

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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On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 106 and a standard deviation of 18. Suppose one individual is randomly chosen. Let X = IQ of an individual. a. What is the distribution of X? X-NO Hint b. Find the probability that a randomly selected person's IQ is over 114. answer to 4 decimal places. Round your c. A school offers special services for all children in the bottom 3% for IQ scores. What is the highest Round your answer to 2 IQ score a child can have and still receive special services? decimal places. d. Find the 25th and 75th percentiles (a.k.a Q1 and Q3) Round your answers to 2 decimal places. Q1: Q3:
Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 40 minutes and standard deviation 16 minutes. A researcher observed 47 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of æ? ¤ - N( c. What is the distribution of ) x? >x - N( d. If one randomly selected student is timed, find the probability that this student's time will be between 41 and 42 minutes. e. For the 47 students, find the probability that their average time studying is between 41 and 42 minutes. f. Find the probability that the randomly selected 47 students will have a total study time more than 1974 minutes. g. For part e) and f), is the assumption of normal necessary? O Yes No h. The top 10% of the total study time for groups of 47 students will be given a sticker that says "Great dedication". What is the least total time that a…
The amount of coffee that people drink per day is normally distributed with a mean of 17 ounces and a standard deviation of 5 ounces. 16 randomly selected people are surveyed. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of ? - N( c. What is the probability that one randomly selected person drinks between 15.5 and 18.5 ounces of coffee per day?
On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 114 and a standard deviation of 16. Suppose one individual is randomly chosen. Let X = IQ of an individual. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected person's IQ is over 112. to 4 decimal places. Round your answer c. A school offers special services for all children in the bottom 6% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places. d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places. Q1: Q3: IQR:
The average amount of money spent for lunch per person in the college cafeteria is $6.96 and the standard deviation is $2.49. Suppose that 7 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N b. What is the distribution of ? ī - N( c. For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $5.8484 and $6.599. d. For the group of 7 patrons, find the probability that the average lunch cost is between $5.8484 and $6.599. e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes
The age of children in kindergarten on the first day of school is uniformly distributed between 4.88 and 5.72 years old. A first time kindergarten child is selected at random. Round answers to 4 decimal places if possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the the child will be older than 5 years old? d. The probability that the child will be between 5.08 and 5.28 years old is e. If such a child is at the 74th percentile, how old is that child? years old.
Suppose the age that children learn to walk is normally distributed with mean 11 months and standard deviation 2 month. 34 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 11 b. What is the distribution of x? a - N( 11 0.3440 c. What is the probability that one randomly selected person learned to walk when the person was between 10.6 and 11.3 months old? 0.1389 d. For the 34 people, find the probability that the average age that they learned to walk is between 10.6 and 11.3 months old. e. For part d), is the assumptiSnter an integer or decimal number, accurate to at least 4 decimal places [more..] f. Find the IQR for the average first time walking age for groups of 34 people. Q1 = months %3D Q3 = months %3D IQR: months Hint: Some Helpful Videos: Finding the Sampling Distribution (+1 Finding a Probability Using the Central Limit Theorem D [+1 Finding Value Given a Probability…
Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 43 minutes and standard deviation 20 minutes. A researcher observed 49 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 43 20 b. What is the distribution of x? ¤ - N( 43 2.8571 v) o c. What is the distribution of æ? x - N( 2107 d. If one randomly selected student is timed, find the probability that this student's time will be 140 between 44 and 47 minutes. .0593 e. For the 49 students, find the probability that their average time studying is between 44 and 47 minutes. .2824 f. Find the probability that the randomly selected 49 students will have a total study time more than 2156 minutes. .3632 g. For part e) and f), is the assumption of normal necessary? NoO Yes o h. The top 20% of the total study time for groups of 49 students will be given a sticker that says "Great…
According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.3 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that the person is between 62 and 63.9 inches. c. The middle 40% of Martian heights lie between what two numbers? Low: inches High: inches
The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 74 minutes and a standard deviation of 17 minutes. Suppose one person at the hot springs is randomly chosen. Let X - the amount of time that person spent at Grover Hot Springs. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N b. Find the probability that a randomly selected person at the hot springs stays longer then 85 minutes. c. The park service is considering offering a discount for the 4% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes. d. Find the Inter Quartile Range (1QR) for time spent at the hot springs. Q1: minutes Q3: minutes IQR: minutes
The amount of coffee that people drink per day is normally distributed with a mean of 16 ounces and a standard deviation of 6 ounces. 35 randomly selected people are surveyed. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of ? - N( c. What is the probability that one randomly selected person drinks between 15.7 and 16.1 ounces of coffee per day? d. For the 35 people, find the probability that the average coffee consumption is between 15.7 and 16.1 ounces of coffee per day. e. For part d), is the assumption that the distribution is normal necessary?O NoO Yes f. Find the IQR for the average of 35 coffee drinkers. Q1 ounces Q3 = ounces IQR: ounces II
Suppose the age that children learn to walk is normally distributed with mean 13 months and standard deviation 1.3 month. 15 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 13 V, 1.3 b. What is the distribution of æ? - N( 13 V, 0.3357 c. What is the probability that one randomly selected person learned to walk when the person was between 11.5 and 14 months old? 0.65483 d. For the 15 people, find the probability that the average age that they learned to walk is between 11.5 and 14 months old. 0.99855 e. For part d), is the assumption that the distribution is normal necessary? Yes No f. Find the IQR for the average first time walking age for groups of 15 people. Q1 = 12.7762 X months %D Q3 13.2238 X months IQR: 0.4476 X months

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