1.)A population of values has a normal distribution with μ=196.8μ=196.8 and σ=63.3σ=63.3. You intend to draw a random sample of size n=121n=121. What is the mean of the distribution of sample means? μ¯x=μx¯= What is the standard deviation of the distribution of sample means? σ¯x=σx¯= Round to 4 decimal places. 2.)A population of values has a normal distribution with μ=70.9μ=70.9 and σ=90.1σ=90.1. You intend to draw a random sample of size n=188n=188. Find the probability that a single randomly selected value is less than 60.4. P(X < 60.4) = Round to 4 decimal places. Find the probability that the sample mean is less than 60.4. P(¯¯¯XX¯ < 60.4) = Round to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted. 3.)A population of values has a normal distribution with μ=30.3μ=30.3 and σ=3σ=3. You intend to draw a random sample of size n=178n=178. Find the probability that a single randomly selected value is between 29.9 and 30.3. P(29.9 < X < 30.3) = Round to 4 decimal places. Find the probability that the sample mean is between 29.9 and 30.3. P(29.9 < ¯¯¯XX¯ < 30.3) = Round to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted. 4.)A population of values has a normal distribution with μ=86.8μ=86.8 and σ=65.8σ=65.8. You intend to draw a random sample of size n=160n=160. Find P4, which is the score separating the bottom 4% scores from the top 96% scores.P4 (for single values) = Find P4, which is the mean separating the bottom 4% means from the top 96% means. P4 (for sample means) = Round to 1 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted. 5.)A manufacturer knows that their items have a normally distributed length, with a mean of 13 inches, and standard deviation of 3.9 inches. If 24 items are chosen at random, what is the probability that their mean length is less than 11.9 inches? Round to 4 decimal places.

1.)A population of values has a normal distribution with μ=196.8μ=196.8 and σ=63.3σ=63.3. You intend to draw a random sample of size n=121n=121. What is the mean of the distribution of sample means? μ¯x=μx¯= What is the standard deviation of the distribution of sample means? σ¯x=σx¯= Round to 4 decimal places. 2.)A population of values has a normal distribution with μ=70.9μ=70.9 and σ=90.1σ=90.1. You intend to draw a random sample of size n=188n=188. Find the probability that a single randomly selected value is less than 60.4. P(X < 60.4) = Round to 4 decimal places. Find the probability that the sample mean is less than 60.4. P(¯¯¯XX¯ < 60.4) = Round to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted. 3.)A population of values has a normal distribution with μ=30.3μ=30.3 and σ=3σ=3. You intend to draw a random sample of size n=178n=178. Find the probability that a single randomly selected value is between 29.9 and 30.3. P(29.9 < X < 30.3) = Round to 4 decimal places. Find the probability that the sample mean is between 29.9 and 30.3. P(29.9 < ¯¯¯XX¯ < 30.3) = Round to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted. 4.)A population of values has a normal distribution with μ=86.8μ=86.8 and σ=65.8σ=65.8. You intend to draw a random sample of size n=160n=160. Find P4, which is the score separating the bottom 4% scores from the top 96% scores.P4 (for single values) = Find P4, which is the mean separating the bottom 4% means from the top 96% means. P4 (for sample means) = Round to 1 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted. 5.)A manufacturer knows that their items have a normally distributed length, with a mean of 13 inches, and standard deviation of 3.9 inches. If 24 items are chosen at random, what is the probability that their mean length is less than 11.9 inches? Round to 4 decimal places.

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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2.)A population of values has a normal distribution with μ=70.9μ=70.9 and σ=90.1σ=90.1. You intend to draw a random sample of size n=188n=188.

Find the probability that a single randomly selected value is less than 60.4.
P(X < 60.4) = Round to 4 decimal places.
Find the probability that the sample mean is less than 60.4.
P(¯¯¯XX¯ < 60.4) = Round to 4 decimal places.

Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.

3.)A population of values has a normal distribution with μ=30.3μ=30.3 and σ=3σ=3. You intend to draw a random sample of size n=178n=178.

Find the probability that a single randomly selected value is between 29.9 and 30.3.
P(29.9 < X < 30.3) = Round to 4 decimal places.
Find the probability that the sample mean is between 29.9 and 30.3.
P(29.9 < ¯¯¯XX¯ < 30.3) = Round to 4 decimal places.

Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.

4.)A population of values has a normal distribution with μ=86.8μ=86.8 and σ=65.8σ=65.8. You intend to draw a random sample of size n=160n=160.

Find P₄, which is the score separating the bottom 4% scores from the top 96% scores.P₄ (for single values) =
Find P₄, which is the mean separating the bottom 4% means from the top 96% means. P₄ (for sample means) =

Round to 1 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.

5.)A manufacturer knows that their items have a normally distributed length, with a mean of 13 inches, and standard deviation of 3.9 inches.

If 24 items are chosen at random, what is the probability that their mean length is less than 11.9 inches?

Round to 4 decimal places.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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