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.

Z is typically used to indicate a standard score, rather than a raw score.

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion between the two Z scores.

To find the probability P(-2.08<z<2.08), where z is the reading in degrees, we can use the standard normal distribution or the z-score.

The z-score represents the number of standard deviations an observation or value is from the mean. It is calculated using the formula:
z = (x - μ) / σ

Where:
- x is the given value,
- μ is the mean of the distribution, and
- σ is the standard deviation.

In this case, the given values are -2.08 and 2.08, which represent the lower and upper limits of the range.

To find the probability, we need to calculate the area under the standard normal curve that falls between -2.08 and 2.08.

Step 1: Calculate the z-scores for -2.08 and 2.08.
z1 = (-2.08 - 0) / 1.00
z2 = (2.08 - 0) / 1.00

Step 2: Look up the corresponding area in the standard normal distribution table (also known as the z-table).

Alternatively, you can use a calculator or statistical software to find the area directly. Most scientific calculators and statistical software have built-in functions for calculating probabilities for the standard normal distribution.

Using the z-table or calculator, we find:
- From the z-table, P(z < -2.08) = 0.0188
- From the z-table, P(z < 2.08) = 0.9812

Step 3: Calculate the desired probability P(-2.08 < z < 2.08).
P(-2.08 < z < 2.08) = P(z < 2.08) - P(z < -2.08)
P(-2.08 < z < 2.08) = 0.9812 - 0.0188 = 0.9624

Therefore, the probability P(-2.08 < z < 2.08) is approximately 0.9624.