A random variable X is normally distributed. It has a mean of 230 and a standard deviation of 31. List the givens with correct symbols: ? v = 230 = 31 a) If you take a sample of size 11, what can you say what the shape of the sampling distribution for the sample mean? Select an answer Because: (Check all that apply) O population is normal On is less than 30 population is not normal On is at least 30 b) For a sample of size 11, state the mean and the standard deviation of the sampling distribution of the sample mean. round to 2 decimals c) Find the probability of getting a sample mean greater than 241.4 when taking a sample of size 11 from this population. P( > 241.4) = round to 2 decimals
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![A random variable X is normally distributed. It has a mean of 230 and a standard deviation of 31.
List the givens with correct symbols:
- Mean (μ) = 230
- Standard deviation (σ) = 31
a) If you take a sample of size 11, what can you say about the shape of the sampling distribution for the sample mean?
- [Dropdown: Select an answer]
Because: (Check all that apply)
- population is normal
- n is less than 30
- population is not normal
- n is at least 30
b) For a sample of size 11, state the mean and the standard deviation of the sampling distribution of the sample mean.
- Mean (μ) =
- Standard deviation (σ) = [Input box] (round to 2 decimals)
c) Find the probability of getting a sample mean greater than 241.4 when taking a sample of size 11 from this population.
- P(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F170e3780-ffa2-4c07-bf27-8e02aea9a195%2F9be414b2-a333-4ec8-a219-29507d71e23d%2Fj7s6cwi_processed.png&w=3840&q=75)
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