find the probability?

Question

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than -1.308°C. Round to 4 decimal places.

Answer 1

z = -1.308

Look at the z-score table!

Answer 2

Hello Madeline,

You know the formula for obtaining a z-score because we have discussed. 

z = x - xbar
     ---------

        sd 


Where x is your value, xbar is your mean and, sd is your standard deviation

z = -1.308 - 0
     -------------
         1.00

z = -1.308
      --------

        1.00

z = -1.308   (But THIS is NOT your answer) Why? You are looking for the probability that the thermometer you randomly pulled is going to yield a reading GREATER than whatever probability is associated with this z score. 


I would personally round your z score up to -1.31. You already have been shown by me how to gather the associated value, however in the event you have forgotten: 

I would round up on your z score to -1.31   Remember 4 and below let it go; 5 and above, give it a shove? 


http://www.z-table.com/


If you look at your table you will see the value which intersects between z being -1.3 and .01 is .0951 

This is why the z score answer is not sufficient. If you were to look up that value on the z score table without rounding you would obtain a different value. That is, if you look at the intersection of 1.3 and .00 that value is .0968. You can see the two values differ. 


Remember the value of .0951 is your four decimal answer.

But your problem is asking what the probability is of obtaining a reading greater than -1.308, correct? 

Therefore, you must subtract that obtained value of .0951 from 1.000 to obtain the correct probability and answer. Why? Because the value we just obtained is for ALL values along the x axis from the obtained value to the left of the bell curve. And you are wanting to know all values associated with that z score and to the right of your bell curve due to the word greater. 


  1.0000
-  .0951
----------

.9049      <--------THIS is your answer to four decimal places. To determine your probability you move your decimal two places to the RIGHT and arrive at the correct answer of 90.49 %. 



Have a great weekend and please let me know that you understand the explanation and answer in a comment below.