List the characteristics of the standardized normal distribution and explain why it is a useful distribution in inferential statistics.
What will be an ideal response?
The characteristics of the standardized normal distribution are as follows:(1) It is symmetrical about its mean.(2) The mean identifies the normal curve's highest point (the mode) and the vertical line about which this normal curve is symmetrical.(3) The normal curve has an infinite number of cases (it is a continuous distribution), and the area under the curve has a probability density equal to 1.0.(4) The standardized normal distribution has a mean of 0 and a standard deviation of 1. The standardized normal distribution is a purely theoretical probability distribution, but it is the most useful distribution in inferential statistics. It is valuable because we can translate, or transform, any normal variable, X, into the standardized value, Z. The standardized normal table in the back of most statistics and marketing research books allows us to evaluate the probability of the occurrence of many events without any difficulty.
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Answer the following statement true (T) or false (F)