Let be a z-score that is unknown but identifiable by position and area. If the symmetrical area between - and + is 0.903, the value of is 1.66.

Question

Let  be a z-score that is unknown but identifiable by position and area. If the symmetrical area between -  and +  is 0.903, the value of  is 1.66.

Quizplus · Accepted Answer

By definition, a z-score represents the number of standard deviations a particular value is from the mean of a distribution. Therefore, the symmetrical area between - z and + z represents the proportion of values in the distribution that fall within z standard deviations from the mean. In this case, the symmetrical area between -11eb6b9e_0663_f20f_8d9d_c9597bca86a9_TB8220_11 and +11eb6b9e_0663_f210_8d9d_8777829065fc_TB8220_11 represents 90.3% of the values in the distribution. Since the z-score corresponding to this area is unknown, it is denoted as 11eb6b9e_0663_cafe_8d9d_cf3057040604_TB8220_11.

If we know that the value of 11eb6b9e_0663_f211_8d9d_dd853fa5564b_TB8220_11 corresponds to a z-score of 1.66, we can use a standard normal distribution table (or a calculator that has a built-in normal distribution function) to determine the area to the left of this value. It turns out that this area is approximately 0.9515, which means that the proportion of values in the distribution that fall between 11eb6b9e_0663_f20f_8d9d_c9597bca86a9_TB8220_11 and 11eb6b9e_0663_f210_8d9d_8777829065fc_TB8220_11 is 0.9515 - (1 - 0.9515) = 0.903, which matches the given information. Therefore, the statement is true.

Let Be a Z-Score That Is Unknown but Identifiable