Assume that thermometer readings are normally distributed with a mean of 0degreesC and a standard deviation of 1.00degreesC. A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the probability of the reading. (The given values are in Celsius degrees.)
Between 0.25 and 1.25
The probability is:
is it 0.2557
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gave me .2956
http://davidmlane.com/normal.html
Enter you data with "between"
To find the probability of the thermometer reading being between 0.25 and 1.25 degrees Celsius, we can use the concept of standard normal distribution.
1. Start by sketching a normal distribution curve with the mean of 0 degrees Celsius and a standard deviation of 1 degree Celsius. The curve should be symmetric and bell-shaped.
2. Identify the range of interest, which is between 0.25 and 1.25 degrees Celsius, on the x-axis of the curve.
3. We need to standardize the values 0.25 and 1.25 to determine their positions on the standardized (z) scale. To do this, we use the formula: z = (x - μ) / σ, where z is the standardized value, x is the original value, μ is the mean, and σ is the standard deviation.
For 0.25: z = (0.25 - 0) / 1 = 0.25
For 1.25: z = (1.25 - 0) / 1 = 1.25
4. Next, we can use a standard normal distribution table or a calculator to find the probabilities associated with the z-values we obtained.
Using a standard normal distribution table, we can find the probability for z = 0.25 and z = 1.25. The probability associated with z = 0.25 is approximately 0.5987, and the probability associated with z = 1.25 is approximately 0.8944.
5. Finally, to find the probability of the reading falling between 0.25 and 1.25 degrees Celsius, we subtract the probability associated with 0.25 from the probability associated with 1.25:
Probability = P(0.25 ≤ X ≤ 1.25) = P(z ≤ 1.25) - P(z ≤ 0.25) = 0.8944 - 0.5987 ≈ 0.2957
Therefore, the probability of the reading being between 0.25 and 1.25 degrees Celsius is approximately 0.2957 or 29.57%.