The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 and a standard deviation of 129 chips.(a) What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips?(b) What is the probability that a randomly selected bag contains fewer than 1100 chocolate chips?(c) What proportion of bags contains more than 1225 chocolate chips?(d) What is the percentile rank of a bag that contains 1450 chocolate chips?To solve these questions, click the icon to view a table of areas under the normal curve.Question (a) specifically asks for the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips. The space provided indicates that the answer should be rounded to four decimal places as needed. **Standard Normal Distribution Table (Z-Table)**This table displays the cumulative probability of the standard normal distribution. The standard normal distribution, often represented by a symmetrical bell curve, is a continuous probability distribution that is symmetric around its mean.### Table V: Standard Normal DistributionThe table provides the area under the standard normal curve to the left of a given Z-value. The Z-values are typically found on the leftmost column and the top row of the table. Each cell shows the cumulative probability associated with that Z-value.#### Reading the Table:- **Z-value:** Find the Z-value to two decimal places using the left column for the first decimal and the top row for the second decimal.- **Probability:** The corresponding cell value is the probability that a standard normal random variable is less than or equal to the given Z-value.For example, a Z-value of -0.5 corresponds to a cumulative probability of 0.3085.### Diagram:The top left part of the image contains a diagram illustrating a normal distribution curve.- **X-axis:** Represents the Z-values.- **Area:** The shaded portion under the curve corresponds to the probability of the random variable falling within that range.- This diagram helps conceptualize how areas under the curve relate to cumulative probabilities.The standard normal distribution is fundamental in statistics, enabling calculations related to areas under the curve, z-scores, and probabilities for a normally distributed dataset.

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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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The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips? (b) What is the probability that a randomly selected bag contains fewer than 1100 chocolate chips? (c) What proportion of bags contains more than 1175 chocolate chips? (d) What is the percentile rank of a bag that contains 1050 chocolate chips? Click the icon to view a table of areas under the normal curve. (a) The probability that a randomly selected bag contains between 1100 and 1500 chocolate chips is 0.8536. (Round to four decimal places as needed.) (b) The probability that a randomly selected bag contains fewer than 1100 chocolate chips is 0.1190. (Round to four decimal places as needed.) (c) The proportion of bags that contains more than 1175 chocolate chips is 0.7258. (Round to four decimal places as needed.) (d) A…
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1000 and 1400 chocolate chips? (b) What is the probability that a randomly selected bag contains fewer than 1000 chocolate chips? (c) What proportion of bags contains more than 1200 chocolate chips? (d) What is the percentile rank of a bag that contains 1025 chocolate chips? Click the icon to view a table of areas under the normal curve. (a) The probability that a randomly selected bag contains between 1000 and 1400 chocolate chips is 0.8493 (Round to four decimal places as needed.) (b) The probability that a randomly selected bag contains fewer than 1000 chocolate chips is 0.0256 (Round to four decimal places as needed.) (c) The proportion of bags that contains more than 1200 chocolate chips is 0.6554 (Round to four decimal places as needed.) (d) A bag…
The amount of money that college students spend on food each week during the academic year is normally distributed with a mean of $31.28 and a standard deviation of $11.42 What is the probability that one randomly selected student will spend less than $25 per week on food? If you randomly select 10 students, what is the probability that their mean will be less than $25?
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips? (b) What is the probability that a randomly selected bag contains fewer than 1025 chocolate chips? (c) What proportion of bags contains more than 1200 chocolate chips? (d) What is the percentile rank of a bag that contains 1025 chocolate chips? View an e Tables of Areas under the Normal Curve Area- .00 .01 Standard Normal Distribution ▬▬ .02 .03 .04 .05 .06 .07 .08 .09 z 0.0003 0.0003 0.0005 0.0005 0.0007 0.0007 -3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002 -3.3 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003 -3.2 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005 -3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0008 0.0007 0.0007 -3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011…
The lengths of lumber a machine cuts are normally distributed with a mean of 105 inches and a standard deviation of 0.7 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 105.37 inches? (b) A sample of 35 boards is randomly selected. What is the probability that their mean length is greater than 105.37 inches?
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 65 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 65 tons and standard deviation ? = 1.7 ton. (a) What is the probability that one car chosen at random will have less than 64.5 tons of coal? (Round your answer to four decimal places.)(b) What is the probability that 37 cars chosen at random will have a mean load weight x of less than 64.5 tons of coal? (Round your answer to four decimal places.)
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips? (b) What is the probability that a randomly selected bag contains fewer than 1100 chocolate chips? (c) What proportion of bags contains more than 1175 chocolate chips? (d) What is the percentile rank of a bag that contains 1050 chocolate chips? Click the icon to view a table of areas under the normal curve. (a) The probability that a randomly selected bag contains between 1100 and 1500 chocolate chips is (Round to four decimal places as needed.) ← (b) The probability that a randomly selected bag contains fewer than 1100 chocolate chips is (Round to four decimal places as needed.) (c) The proportion of bags that contains more than 1175 chocolate chips is (Round to four decimal places as needed.) (d) A bag that contains 1050…
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1000 and 1400 chocolate chips? (b) What is the probability that a randomly selected bag contains fewer than 1000 chocolate chips? (c) What proportion of bags contains more than 1200 chocolate chips? (d) What is the percentile rank of a bag that contains 1050 chocolate chips? Click the icon to view a table of areas under the normal curve.
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1000 and 1400 chocolate chips? (b) What is the probability that a randomly selected bag contains fewer than 1000 chocolate chips? (c) What proportion of bags contains more than 1200 chocolate chips? (d) What is the percentile rank of a bag that contains 1475 chocolate chips? Click the icon to view a table of areas under the normal curve. ..... (a) The probability that a randomly selected bag contains between 1000 and 1400 chocolate chips is (Round to four decimal places as needed.) (b) The probability that a randomly selected bag contains fewer than 1000 chocolate chips is (Round to four decimal places as needed.) (c) The proportion of bags that contains more than 1200 chocolate chips is (Round to four decimal places as needed.) (d) A bag that contains…
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1000 and 1400 chocolate chips, inclusive? (b) What is the probability that a randomly selected bag contains fewer than 1100 chocolate chips? (c) What proportion of bags contains more than 1225 chocolate chips? (d) What is the percentile rank of a bag that contains 1450 chocolate chips? (a) The probability that a randomly selected bag contains between 1000 and 1400 chocolate chips, inclusive, is. (Round to four decimal places as needed.)
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 54 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 54 tons and standard deviation ? = 1.4 ton. (a) What is the probability that one car chosen at random will have less than 53.5 tons of coal? (Round your answer to four decimal places.)(b) What is the probability that 26 cars chosen at random will have a mean load weight x of less than 53.5 tons of coal? (Round your answer to four decimal places.)(c) Suppose the weight of coal in one car was less than 53.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? YesNo Suppose the weight of coal in 26 cars selected at random had an average x of less than 53.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? Yes, the probability that this deviation…
K The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1100 and 1400 chocolate chips, inclusive? (b) What is the probability that a randomly selected bag contains fewer than 1000 chocolate chips? (c) What proportion of bags contains more than 1200 chocolate chips? (d) What is the percentile rank of a bag that contains 1425 chocolate chips? (a) The probability that a randomly selected bag contains between 1100 and 1400 chocolate chips, inclusive, is (Round to four decimal places as needed.) (b) The probability that a randomly selected bag contains fewer than 1000 chocolate chips is (Round to four decimal places as needed.) (c) The proportion of bags that contains more than 1200 chocolate chips is (Round to four decimal places as needed.) (d) A bag that contains 1425 chocolate chips is in the…

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