The alternate of normal distribution if population variance is unknown.

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Answer 1

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, Problem 1FP

To determine

To find: The alternate of normal distribution if population variance is unknown.

Expert Solution & Answer

Answer to Problem 1FP

T distribution

Explanation of Solution

By definition, the normal distribution is symmetrical in nature with same mean, median and mode. As it is symmetric so its skewness is zero. The population variance and population mean are known for normal distribution. But when the sample size is small and population variance is not known, then normal distribution could not be used.

One such distribution which is similar to normal distribution is t distribution. It is denoted by X¯−μsn~tdf=n−1 where, X¯,μ,s,n denote sample mean, population mean, sample standard deviation and sample size respectively. T distribution is also bell shaped and do not require population standard deviation as it is difficult to find the variance of the whole population. The only major difference between the two is that T distribution is heavier on tails than normal distribution. This means that the sample values are quite far from sample mean.

Therefore, T distribution can be used when population variance is unknown.

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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, Problem 1FP

To determine

To find: The alternate of normal distribution if population variance is unknown.

Expert Solution & Answer

Answer to Problem 1FP

T distribution

Explanation of Solution

By definition, the normal distribution is symmetrical in nature with same mean, median and mode. As it is symmetric so its skewness is zero. The population variance and population mean are known for normal distribution. But when the sample size is small and population variance is not known, then normal distribution could not be used.

One such distribution which is similar to normal distribution is t distribution. It is denoted by X¯−μsn~tdf=n−1 where, X¯,μ,s,n denote sample mean, population mean, sample standard deviation and sample size respectively. T distribution is also bell shaped and do not require population standard deviation as it is difficult to find the variance of the whole population. The only major difference between the two is that T distribution is heavier on tails than normal distribution. This means that the sample values are quite far from sample mean.

Therefore, T distribution can be used when population variance is unknown.

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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, Problem 1FP

To determine

To find: The alternate of normal distribution if population variance is unknown.

Expert Solution & Answer

Answer to Problem 1FP

T distribution

Explanation of Solution

By definition, the normal distribution is symmetrical in nature with same mean, median and mode. As it is symmetric so its skewness is zero. The population variance and population mean are known for normal distribution. But when the sample size is small and population variance is not known, then normal distribution could not be used.

One such distribution which is similar to normal distribution is t distribution. It is denoted by X¯−μsn~tdf=n−1 where, X¯,μ,s,n denote sample mean, population mean, sample standard deviation and sample size respectively. T distribution is also bell shaped and do not require population standard deviation as it is difficult to find the variance of the whole population. The only major difference between the two is that T distribution is heavier on tails than normal distribution. This means that the sample values are quite far from sample mean.

Therefore, T distribution can be used when population variance is unknown.

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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, Problem 1FP

To determine

To find: The alternate of normal distribution if population variance is unknown.

Expert Solution & Answer

Answer to Problem 1FP

T distribution

Explanation of Solution

By definition, the normal distribution is symmetrical in nature with same mean, median and mode. As it is symmetric so its skewness is zero. The population variance and population mean are known for normal distribution. But when the sample size is small and population variance is not known, then normal distribution could not be used.

One such distribution which is similar to normal distribution is t distribution. It is denoted by X¯−μsn~tdf=n−1 where, X¯,μ,s,n denote sample mean, population mean, sample standard deviation and sample size respectively. T distribution is also bell shaped and do not require population standard deviation as it is difficult to find the variance of the whole population. The only major difference between the two is that T distribution is heavier on tails than normal distribution. This means that the sample values are quite far from sample mean.

Therefore, T distribution can be used when population variance is unknown.

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Answer 5

Chapter 8, Problem 1FP

To determine

To find: The alternate of normal distribution if population variance is unknown.

Expert Solution & Answer

Answer to Problem 1FP

T distribution

Explanation of Solution

By definition, the normal distribution is symmetrical in nature with same mean, median and mode. As it is symmetric so its skewness is zero. The population variance and population mean are known for normal distribution. But when the sample size is small and population variance is not known, then normal distribution could not be used.

One such distribution which is similar to normal distribution is t distribution. It is denoted by X¯−μsn~tdf=n−1 where, X¯,μ,s,n denote sample mean, population mean, sample standard deviation and sample size respectively. T distribution is also bell shaped and do not require population standard deviation as it is difficult to find the variance of the whole population. The only major difference between the two is that T distribution is heavier on tails than normal distribution. This means that the sample values are quite far from sample mean.

Therefore, T distribution can be used when population variance is unknown.

Answer 6

Chapter 8, Problem 1FP

To determine

To find: The alternate of normal distribution if population variance is unknown.

Expert Solution & Answer

Answer to Problem 1FP

T distribution

Explanation of Solution

By definition, the normal distribution is symmetrical in nature with same mean, median and mode. As it is symmetric so its skewness is zero. The population variance and population mean are known for normal distribution. But when the sample size is small and population variance is not known, then normal distribution could not be used.

One such distribution which is similar to normal distribution is t distribution. It is denoted by X¯−μsn~tdf=n−1 where, X¯,μ,s,n denote sample mean, population mean, sample standard deviation and sample size respectively. T distribution is also bell shaped and do not require population standard deviation as it is difficult to find the variance of the whole population. The only major difference between the two is that T distribution is heavier on tails than normal distribution. This means that the sample values are quite far from sample mean.

Therefore, T distribution can be used when population variance is unknown.

Answer 7

Chapter 8, Problem 1FP

To determine

To find: The alternate of normal distribution if population variance is unknown.

Answer 8

Expert Solution & Answer

Answer to Problem 1FP

T distribution

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

By definition, the normal distribution is symmetrical in nature with same mean, median and mode. As it is symmetric so its skewness is zero. The population variance and population mean are known for normal distribution. But when the sample size is small and population variance is not known, then normal distribution could not be used.

One such distribution which is similar to normal distribution is t distribution. It is denoted by X¯−μsn~tdf=n−1 where, X¯,μ,s,n denote sample mean, population mean, sample standard deviation and sample size respectively. T distribution is also bell shaped and do not require population standard deviation as it is difficult to find the variance of the whole population. The only major difference between the two is that T distribution is heavier on tails than normal distribution. This means that the sample values are quite far from sample mean.

Therefore, T distribution can be used when population variance is unknown.

Answer 12

Ch. 8 - Prob. 1FP Ch. 8 - Prob. 2FP Ch. 8 - Prob. 3FP Ch. 8 - Prob. 4FP Ch. 8 - Prob. 5FP Ch. 8 - Prob. 6FP Ch. 8 - Prob. 7FP Ch. 8 - Prob. 8FP Ch. 8 - Prob. 9FP Ch. 8 - Prob. 10FP

The alternate of normal distribution if population variance is unknown.

Solution Summary: The author explains that normal distribution is symmetrical in nature and its skewness is zero. However, when the sample size is small and population variance is not known, t distribution can be used.

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To find: The alternate of normal distribution if population variance is unknown.

Answer to Problem 1FP

Explanation of Solution

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Chapter 8 Solutions