Please, answer with the full solution! Thanks for the help!

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:

• Less than 0.53.
• Greater than -0.11
• Greater than -1.11
• Between 1.00 and 2.25
• Between -2.28 and -1.76
• Between -1.33 and 1.86
• Greater than 1.71

Answer 1

All of the answers come from reading the Z-table. Z-tables give you the probability that you would randomly find a value less than some given value, assuming that the distribution has a mean of 0 and standard deviation of 1. Since our given distribution (reading on a thermometer) already fits that criteria, we can just look up the values given on a z-table.

 

From the Z-table:

 

P(z<.53) = 0.7019

 

So our first answer is 0.7019.

 

P(z<-.11) = 0.4562

 

So our second answer is 1-0.4562 = .5438 (It wanted the probability z>0.11)

 

Third answer is 0.8665.

 

Fourth answer is between 1.00 and 2.25, so

 

P(z<2.25) - P(z<1.00) = 0.9878 - 0.8413 = 0.1465

 

Fifth answer is 0.0392 - 0.0113 = 0.0279.

 

Sixth answer is 0.8768.

 

Last answer is 0.0436.

 

 

 

Here they are again, for ease of reading:

1) 0.7019

2) 0.5438

3) 0.8665

4) 0.1465

5) 0.0279

6) 0.8768

7) 0.0436