The expected value of the standard normal distribution is equal to the total amount of the value. It is usually equal to it when the value works out to be the same.
One standard deviation
Because as the sample size increases the Student's t-distribution approaches the standard normal.
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.
Yes.
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.
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.
One standard deviation
The mean, median, and mode of a normal distribution are equal; in this case, 22. The standard deviation has no bearing on this question.
Because as the sample size increases the Student's t-distribution approaches the standard normal.
Only the mean, because a normal distribution has a standard deviation equal to the square root of the mean.
The answer will depend on the underlying distribution for the variable. You may not simply assume that the distribution is normal.
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.
false
-1.43 (approx)
z = 1.52 (approx)
A normal distribution is a symmetric, bell-shaped curve characterized by its mean and standard deviation. Approximately 68% of the data falls within one standard deviation from the mean, about 95% within two standard deviations, and around 99.7% within three standard deviations, commonly referred to as the empirical rule. Additionally, the mean, median, and mode of a normal distribution are all equal and located at the center of the distribution. This property makes the normal distribution fundamental in statistics and probability theory.
Yes, it is true; and the 2 quantities that describe a normal distribution are mean and standard deviation.