The z-scores that bound the middle 35 % under the standard normal curve are z = -a and z = a. Find the value of a.
Write only a positive number as your answer. Round to two decimal places (for example: 0.81).
You are looking for ± .175 on the table.
To find the value of "a" that corresponds to the middle 35% under the standard normal curve, we need to find the z-scores that bound this area.
First, we need to determine the z-score that represents the lower 17.5% of the distribution. This is half of the 35% (middle 35% is divided into two equal parts).
To find this z-score, we can use a standard normal distribution table or a calculator that provides the cumulative distribution function for the standard normal distribution.
Using a standard normal distribution table, we find that the z-score corresponding to the lower 17.5% is approximately -0.92.
Next, we need to find the z-score that represents the upper 17.5% of the distribution. Since the standard normal distribution is symmetrical, this z-score will have the same magnitude as the lower z-score but with a positive sign.
So, the upper z-score is 0.92.
Finally, since the problem states that z = -a and z = a, we can take either the lower or upper z-score to find the value of "a".
In this case, we can use the lower z-score, which is -0.92, to get the value of "a".
Therefore, the value of "a" is 0.92 (rounding to two decimal places).