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The sample mean is an estimator that will consistently have an approximately normal distribution, particularly due to the Central Limit Theorem. As the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the original population's distribution, provided the samples are independent and identically distributed. This characteristic makes the sample mean a robust estimator for large sample sizes.
What else can I help you with?
What describes the shape of a distribution which is approximately normal?
A "bell" shape.
Is 1.4 unusual in z-score?
No. If the underlying distribution is approximately Normal then 1.4 is not at all unusual.
What proportion of a normal distribution corresponds to z-scores greater than plus 1.04?
To find the proportion of a normal distribution corresponding to z-scores greater than +1.04, you can use the standard normal distribution table or a calculator. The area to the left of z = 1.04 is approximately 0.8508. Therefore, the proportion of the distribution that corresponds to z-scores greater than +1.04 is 1 - 0.8508, which is approximately 0.1492, or 14.92%.
What you mean by saying random variable is approximately normally distributed?
Exactly "what it says on the tin"! The distribution is nearly, but not quite, the standard normal, or Gaussiam distribution.
Does a normal probability distribution include a bimodal distribution?
No, the normal distribution is strictly unimodal.
What describes the shape of a distribution which is approximately normal?
A "bell" shape.
Is 1.4 unusual in z-score?
No. If the underlying distribution is approximately Normal then 1.4 is not at all unusual.
Why is the Gaussian distribution referred to as normal distribution?
Because many naturally occurring variables were approximately distributed according to a Normal bell shaped curve.Because many naturally occurring variables were approximately distributed according to a Normal bell shaped curve.Because many naturally occurring variables were approximately distributed according to a Normal bell shaped curve.Because many naturally occurring variables were approximately distributed according to a Normal bell shaped curve.
What you mean by saying random variable is approximately normally distributed?
Exactly "what it says on the tin"! The distribution is nearly, but not quite, the standard normal, or Gaussiam distribution.
What is the difference between a normal distribution and the standard normal distribution?
The standard normal distribution is a normal distribution with mean 0 and variance 1.
What is the difference of a normal distribution and a stardard normal distribution?
The standard normal distribution is a special case of the normal distribution. The standard normal has mean 0 and variance 1.
Is continuous distribution normal distribution?
le standard normal distribution is a normal distribution who has mean 0 and variance 1
What proportion of the scores in a normal distribution is approximately between z -1.16 and z 1.16?
Between z = -1.16 and z = 1.16 is approx 0.7540 (or 75.40 %). Which means ¾ (0.75 or 75%) of the normal distribution lies between approximately -1.16 and 1.16 standard deviations from the mean.
When can you say the distribution is considered normal?
When its probability distribution the standard normal distribution.
Does a normal probability distribution include a bimodal distribution?
No, the normal distribution is strictly unimodal.
Is the normal distribution infinite?
The domain of the normal distribution is infinite.
How does standard normal distribution differ from normal distribution?
The standard normal distribution has a mean of 0 and a standard deviation of 1.
