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What else can I help you with?
Area to the left of the mean in a normal distribution is equal to?
One standard deviation
Why is t score equal to z score in a normal distribution?
Because as the sample size increases the Student's t-distribution approaches the standard normal.
The total area under a normal distribution is infinite?
The total area under a normal distribution is not infinite. The total area under a normal distribution is a continuous value between any 2 given values. The function of a normal distribution is actually defined such that it must have a fixed value. For the "standard normal distribution" where μ=0 and σ=1, the area under the curve is equal to 1.
Are the mean and median equal in a normal distribution?
Yes.
Can normal distribution be applied on discrete data?
Yes. The normal distribution is used to approximate a binomial distribution when the sample size (n) times the probability of success (p), and the probability of failure (q) are both greater than or equal to 5. The mean of the normal approximation is n*p and the standard deviation is the square root of n*p*q.
Is the mean of a standard normal distribution is always equal to 1?
No, the mean of a standard normal distribution is not equal to 1; it is always equal to 0. A standard normal distribution is characterized by a mean of 0 and a standard deviation of 1. This distribution is used as a reference for other normal distributions, which can have different means and standard deviations.
What is the perfect standard normal distribution?
The standard normal distribution is a subset of a normal distribution. It has the properties of mean equal to zero and a standard deviation equal to one. There is only one standard normal distribution and no others so it could be considered the "perfect" one.
Is the standard deviation of standard normal distribution alway equal to 1?
Yes, the standard deviation of a standard normal distribution is always equal to 1. The standard normal distribution is a specific normal distribution with a mean of 0 and a standard deviation of 1, which allows it to serve as a reference for other normal distributions. This property is essential for standardizing scores and facilitating comparisons across different datasets.
Area to the left of the mean in a normal distribution is equal to?
One standard deviation
What are the median and mode of a normal distribution if the mean is 22 and the standard deviation is 4?
The mean, median, and mode of a normal distribution are equal; in this case, 22. The standard deviation has no bearing on this question.
What information do you need to calculate a probability with a normal distribution?
Only the mean, because a normal distribution has a standard deviation equal to the square root of the mean.
Why is t score equal to z score in a normal distribution?
Because as the sample size increases the Student's t-distribution approaches the standard normal.
When the population standard deviation is unknown the sampling distribution is equal to what?
The answer will depend on the underlying distribution for the variable. You may not simply assume that the distribution is normal.
If the mean of a normal distribution i s105 what is the median of the distribution?
In a normal distribution, the mean, median, and mode are all equal. Therefore, if the mean of the distribution is 105, the median of the distribution is also 105. This property holds true for any normal distribution regardless of its standard deviation.
Is the middle spread that is the middle 50 percent of the normal distribution is equal to one standard deviation?
false
What does it mean if the standard deviation equal to one and the mean is equal to zero?
If the standard deviation is equal to one and the mean is equal to zero, it indicates that the data is centered around zero and has a consistent spread. Specifically, this situation often describes a standard normal distribution (also known as a z-distribution), where approximately 68% of the data falls within one standard deviation of the mean. Therefore, most of the data points are expected to lie between -1 and 1. This standardization is useful for comparing different datasets.
What value of Z from the standard normal distribution table has an area to the left probability equal to 0.0764?
-1.43 (approx)
