To find the temperature reading that separates the bottom 98.3% from the top 1.7% in a normal distribution with a mean of 0 degrees Celsius and a standard deviation of 1 degree Celsius, we need to find the z-score corresponding to the 98.3rd percentile.
You can use a z-table or a standard normal distribution calculator to find the z-score. The z-score represents the number of standard deviations away from the mean a particular value is.
- Since we are looking for the 98.3 percentile, we need to find the z-score that corresponds to a cumulative probability of 0.983.
Using a z-table or a calculator:
- The z-score that corresponds to 0.983 is approximately 2.17 (rounded to two decimal places).
- Now we can find the temperature reading corresponding to this z-score using the formula:
\[ X = \mu + (Z \times \sigma) \]
Where:
- \(X\) = the value from the normal distribution
- \(\mu\) = mean = 0
- \(Z\) = z-score = 2.17
- \(\sigma\) = standard deviation = 1
Putting in the values:
\[ X = 0 + (2.17 \times 1) = 2.17 \]
Thus, the temperature reading that separates the bottom 98.3% from the top 1.7% is 2.17 degrees Celsius (rounded to the nearest hundredth).
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