Probability Statistics 1

Question

Readings on a thermometer are normally distributed with a mean of 0C° and a standard deviation of 1.00.


What is the probability that a randomly selected thermometer reads:

a. Less than 0.53. 

b. Greater than -1.11 

c. Between 1.00 and 2.25 

d. Greater than 1.71 

e. Less than -0.23 or greater than 0.23 

Answer 1

Hi Star-Asia,

 

Do you have a table of the standard normal curve z-scores?  Do you have a graph of the standard normal curve?

 

You need these to solve this problem.  I do not have one here at home, but I can show you how to set these up...

 

Because your mean = 0 and your standard deviation = 1, all of your numbers are already z-scores.  If this had not been the case, you would have to convert your numbers to z-scores before continuing to do these steps.

 

The table of z-scores has numbers in one column on the left and numbers in one row across the top.  The numbers along the left are how the number starts, and the numbers on the top are how the numbers finish.  Meaning, if the leftmost column has a 2.1, then the top column that reads "00" means the cell (the number you are looking for) where this"2.1"  row and the "00" column meet, the z-score is 2.100, if you go across the 2.1 row to the "23" column, that z-score would be 2.123.

 

So for your problems, look up:

 

(a)  0.53 in the table, this is the probability.

(b)  Calculate:  1 - (the lookup value for -1.11)

(c)  Calculate: (Look up value for 2.25) - (look up value for 1.00)

(d)  Calculate:  1 - (lookup value for 1.71)

(e)  The "less than", look up the value for -0.23.  For the "greater than" calculate:  1-(look up value for 0.23), then add these two numbers together.