assume the readings on thermometers are normally distributed with a mean of 0 C and a standard deviation of 1.00 C. Find the probability P(-2.08<z<2.08), where z is the reading in degrees.
Enter your values here, (I don't see the difference between a page like this and using tables)
http://davidmlane.com/normal.html
I got 0.9625
To find the probability P(-2.08 < z < 2.08), where z is the reading in degrees, we need to calculate the cumulative probability between these two z-values.
Step 1: Standardize the z-values
Since we know that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C, we can calculate the z-values using the formula:
z = (x - mean) / standard deviation
For the lower bound of -2.08:
z1 = (-2.08 - 0) / 1.00 = -2.08
For the upper bound of 2.08:
z2 = (2.08 - 0) / 1.00 = 2.08
Step 2: Look up the cumulative probability
Once we have the standardized z-values, we can look up the cumulative probability associated with those z-values in a standard normal distribution table or use a statistical calculator.
Using a standard normal distribution table, we can find the area under the curve between -2.08 and 2.08.
From the table, we find that the cumulative probability for z = -2.08 is approximately 0.0188, and the cumulative probability for z = 2.08 is approximately 0.9821.
Step 3: Calculate the probability
To find the probability between -2.08 and 2.08, we subtract the cumulative probability for the lower bound from the cumulative probability for the upper bound:
P(-2.08 < z < 2.08) = P(z < 2.08) - P(z < -2.08)
= 0.9821 - 0.0188
= 0.9633
Therefore, the probability P(-2.08 < z < 2.08) is approximately 0.9633.