Question 1182375
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x = temperature in degrees Celsius
mu = 0 = population mean temperature in degrees C
sigma = 0.9 = population standard deviation for the temperatures


Convert x = 0.5 to a corresponding z score
z = (x-mu)/sigma
z = (0.5-0)/0.9
z = 0.56 approximately


Do the same for x = 1.6
z = (x-mu)/sigma
z = (1.6-0)/0.9
z = 1.78 approximately


Your teacher is asking you to find P(0.5 < x < 1.6) which is roughly equivalent to P(0.56 < z < 1.78) based on those earlier z score conversions.


Now use a z table such as this one
<a href = "https://www.ztable.net/">https://www.ztable.net/</a> 
or one you would find in the back of your textbook. 


From that table, we see the following approximations
P(z < 0.56) = 0.71226
P(z < 1.78) = 0.96246
which are found as shown below
<img width="50%" src = "https://i.imgur.com/FPZZT8w.png">
the stuff in red pertains to z = 0.56, while the stuff in blue is for z = 1.78


Then we subtract those values to get the answer we're after
P(a < z < b) = P(z < b) - P(z < a)
P(0.56 < z < 1.78) = P(z < 1.78) - P(z < 0.56)
P(0.56 < z < 1.78) = 0.96246 - 0.71226
P(0.56 < z < 1.78) = 0.2502
P(0.5 < x < 1.6) = 0.2502


Answer: Approximately 0.2502
Use a calculator to get more accuracy.


There's roughly a 25.02% chance of getting a reading between 0.5 degrees C and 1.6 degrees C (when the true reading should be 0 degrees C).
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