Question

What proportion of a normal distribution is located between z = 0 and z = +1.50?​ ​0.4332 ​0.8664 ​0.0668 ​0.9332?

Answer 1

0.4332 The problem is asking what proportion of a normal distribution is within 1.50 standard deviations on the positive half of the curve. So let's take a look. First thing is to figure out what would be a reasonable answer. Looking at the standard deviation, there will be 34.1% within 0 to +1 standard deviations. And there will be 47.7% within 2 standard deviations. So the correct answer will be something between 0.341 and 0.477. So let's look at the possible answers. ​0.4332 - This answer falls within the desired range. It's a candidate. ​0.8664 - This answer is way too large. Well over 50%, so it can't work. ​0.0668 - This answer is way too small. So once again, it can't work ​0.9332 - If the 0.8664 above was too large, imagine how unreasonable this answer is. Also wrong. So of the 4 available choices, only 0.4332 is possible. So that's the correct answer.