Question

Here’s a fun experiment to try on your friends. Show them a picture of the same line segment for about 1 second. Then, ask each person to draw a line segment congruent to the one they saw. For each person, you can calculate (reproduction length) − (original length). It turns out, the errors are normally distributed with mean 0 (some people underestimate the true length, some overestimate it). Indeed, it is so common that error ideas are normally distributed that this is where the “normal” curve got its name (normal, as in common or routine). If you know that 6% of people will draw the segment too long by 3 cm or more in this experiment, what is the standard deviation in the errors?

Answer 1

Solution:

Given: the errors are normally distributed with mean 0 (some people underestimate the true length, some overestimate it).

That is:

6% of people will draw the segment too long by 3 cm or more in this experiment

That is:  

that is:

We have to find the standard deviation in the errors.

First find z value such that:

that is find z such that:

Look in z table for area 0.9400 or its closest area and find z value.

Area 0.9400 is between 0.9394 and 0.9406 and both the area are at same distance from 0.9400

thus we find both z values and then find their average.

for area 0.9394 , z = 1.55

for area 0.9406 , z = 1.56

Thus Average of z values = (1.55+1.56) / 2 = 1.555

Thus required z value = 1.555

Now use following z score formula to find standard deviation:

Thus the standard deviation in the errors is