1. Explain what it means for the normal distribution to be symmetrical about the mean? 2....

1. Explain what it means for the normal distribution to be symmetrical about the mean?

2. Why is it important to know the mean and standard deviation for a data set when applying the empirical rule?

3. If we are focused on 68% of the normal distribution, what percentage of the distribution is left in the upper tail only?

4. What value separates the 50% of the distribution from the other 50% of the distribution?

Expert Solution

(1)

The normal distribution to be symmetrical about the mean means the left side of the distribution mirrors the right side. It is a never a skewed distribution. It is unimodal.

(2)

It is important to know the mean and standard deviation for a data set when applying the empirical rule because the empirical rule requires the mean ad standard deviation as follows:

The empirical rule states that for a normal distribution, nearly all of the data will fall within 3 standard deviation of themean:

68% of data falls within first standard deviation from the mean.

95% of data falls within two standard deviation from the mean.

99.7% of data falls within three standard deviation from the mean.

(3)

If we are focused on 68% of the normal distribution percentage of the distribution is left in the upper tail only = (100- 68)/2 = 16%

(4) The value = mean seperates the 50% of the distribution from the other 50% of the distribution.

milcah answered 1 day ago

A bimodal distribution may never be what? 1. symmetrical 2. a frequency distribution 3. normal 4....

A bimodal distribution may never be what? 1. symmetrical 2. a frequency distribution 3. normal 4. all of these

11. In SPC, the distribution of “sample means” 1) Cannot be approximated by normal distribution. 2)...

11. In SPC, the distribution of “sample means” 1) Cannot be approximated by normal distribution. 2) Will have greater variability than the process distribution. 3) Will have a mean greater than the process distribution as a function of the sample size. 4) Is exactly like the original distribution under all circumstances. 5) None of the above is true. 15. Which of the following statements is true? Training of Service Personnel is a criterion for evaluating the explicit servicesfeature of the...

1. What is the mean and standard deviation associated with the standard normal distribution? 2. Use...

1. What is the mean and standard deviation associated with the standard normal distribution? 2. Use the standard normal distribution table to calculate the following probabilities A) P (z ≤ -1.64) B) P (z ≤ 2.11) C) P (z ≥ 0.73) D) P (-1.31 ≤ z ≤ -0.32) 3. Use the standard normal distribution table to find the z-value for each of the following A) P (z ≤ ?) = 0.9495 B) P (z ≤ ?) = 0.2810 C) P...

1. Explain the Bell-shaped curve? 2. What is the difference between the Normal Distribution and the...

1. Explain the Bell-shaped curve? 2. What is the difference between the Normal Distribution and the Standard Normal Distribution?

What is a normal distribution? Draw and label a graph of a normal distribution and explain...

What is a normal distribution? Draw and label a graph of a normal distribution and explain the relevant terms. How can the mean and standard deviation be used to predict outcomes according to this distribution?

The mean of a normal probability distribution is 460; the standard deviation is 6. a. About...

The mean of a normal probability distribution is 460; the standard deviation is 6. a. About 68% of the observations lie between what two values? Lower Value Upper Value b. About 95% of the observations lie between what two values? Lower Value Upper Value c. Nearly all of the observations lie between what two values? Lower Value Upper Value

Suppose that y has a normal distribution with mean 1 and variance 9. What is the...

Suppose that y has a normal distribution with mean 1 and variance 9. What is the probability that y is in the interval [.7, 2.5]?

What is the standard deviation of the standard normal distribution? What is the mean of the...

What is the standard deviation of the standard normal distribution? What is the mean of the standard normal distribution? All symmetric distributions are normal distributions. True or false? Assume body temperature scores are normally distributed in the population with a mean of 36.81°C and a standard deviation of 0.41°C. A person's body temperature is 37.33°C. Calculate their z-score. (Round answer to 2 decimal places) Calculate the z-score for a person who has a body temperature of 35.72°C. (Round answer to...

NORMAL DISTRIBUTION 1. 1A. Which of the following statements are TRUE about the Normal Distribution? Check...

NORMAL DISTRIBUTION 1. 1A. Which of the following statements are TRUE about the Normal Distribution? Check all that apply. The distribution is symmetric with a single peak. 50% of the data values lie at or above the mean. Data values are spread evenly around the mean. The graph of the Normal Distribution is bell-shaped, with tapering tails that never actually touch the horizontal axis. The mean, median and mode are all equal and occur at the center of the distribution....

1. Suppose X follows the normal distribution with mean μ and variance σ^2 . Then: (Circle...

1. Suppose X follows the normal distribution with mean μ and variance σ^2 . Then: (Circle all that apply.) A. X is symmetric with respect to the y-axis. B. P(X=2)=P(X=-2). C. Y=aX follows the same distribution as X, where a is a constant. D. None of the above statements is correct. 2. Given a random variable X having a normal distribution with μ=50, and σ=10. The probability that Z assumes a value between 45 and 62 is: ___________. 3. Which...

Question