The sampling distribution of x ¯

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Answer 1

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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.

Chapter 8.1, Problem 16AYU

(a)

To determine

The sampling distribution of x¯

(b)

To determine

The probability

(c)

To determine

The probability

(d)

To determine

The probability that the value of the sample mean x¯ lies between 59.8 and 65.9

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Client 1 Weight before diet (pounds) Weight after diet (pounds) 128 120 2 131 123 3 140 141 4 178 170 5 121 118 6 136 136 7 118 121 8 136 127 a) Determine the mean change in patient weight from before to after the diet (after – before). What is the 95% confidence interval of this mean difference?

In order to find probability, you can use this formula in Microsoft Excel: The best way to understand and solve these problems is by first drawing a bell curve and marking key points such as x, the mean, and the areas of interest. Once marked on the bell curve, figure out what calculations are needed to find the area of interest. =NORM.DIST(x, Mean, Standard Dev., TRUE). When the question mentions “greater than” you may have to subtract your answer from 1. When the question mentions “between (two values)”, you need to do separate calculation for both values and then subtract their results to get the answer. 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…

If a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by creating a chart. Clearly mark the range, identifying the lower and upper…

Answer 2

Question

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.

Chapter 8.1, Problem 16AYU

(a)

To determine

The sampling distribution of x¯

(b)

To determine

The probability

(c)

To determine

The probability

(d)

To determine

The probability that the value of the sample mean x¯ lies between 59.8 and 65.9

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

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.

Chapter 8.1, Problem 16AYU

(a)

To determine

The sampling distribution of x¯

(b)

To determine

The probability

(c)

To determine

The probability

(d)

To determine

The probability that the value of the sample mean x¯ lies between 59.8 and 65.9

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

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.

Chapter 8.1, Problem 16AYU

(a)

To determine

The sampling distribution of x¯

(b)

To determine

The probability

(c)

To determine

The probability

(d)

To determine

The probability that the value of the sample mean x¯ lies between 59.8 and 65.9

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 8.1, Problem 16AYU

(a)

To determine

The sampling distribution of x¯

(b)

To determine

The probability

(c)

To determine

The probability

(d)

To determine

The probability that the value of the sample mean x¯ lies between 59.8 and 65.9

Answer 6

Chapter 8.1, Problem 16AYU

(a)

To determine

The sampling distribution of x¯

Answer 7

Chapter 8.1, Problem 16AYU

(a)

To determine

The sampling distribution of x¯

Answer 8

(b)

To determine

The probability

Answer 9

(b)

To determine

The probability

Answer 10

(c)

To determine

The probability

Answer 11

(c)

To determine

The probability

Answer 12

(d)

To determine

The probability that the value of the sample mean x¯ lies between 59.8 and 65.9

Answer 13

(d)

To determine

The probability that the value of the sample mean x¯ lies between 59.8 and 65.9

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 8.1 - 1. The ________ ________ of the sample mean, , is...Ch. 8.1 - Prob. 2AYU Ch. 8.1 - 3. The standard deviation of the sampling...Ch. 8.1 - 4. True or False: The distribution of the sample...Ch. 8.1 - Prob. 5AYU Ch. 8.1 - Prob. 6AYU Ch. 8.1 - 7. A simple random sample of size n = 10 is...Ch. 8.1 - 8. A simple random sample of size n = 40 is...Ch. 8.1 - In Problems 9–12, determine and from the given...Ch. 8.1 - Prob. 10AYU

The sampling distribution of x ¯

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The sampling distribution of x¯

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The probability that the value of the sample mean x¯ lies between 59.8 and 65.9

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