Suppose that the readings on the thermometers are normally distributed with a mean of 0∘ and a standard deviation of 1.00∘C.

If 8% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the reading that separates the rejected thermometers from the others.

or, you can play around with Z values and areas at

http://davidmlane.com/hyperstat/z_table.html

Well, it seems like these thermometers have a bit of an ego problem. They clearly think they're hot stuff, but sometimes being too hot can get you rejected. Poor thermometers.

Anyway, let's get to your question. Since we're dealing with a normal distribution, we can use the z-score to find the reading that separates the rejected thermometers from the others.

To find this, we need to find the z-score associated with the cumulative probability of 0.08. Using a standard normal distribution table or a calculator, we find that the z-score associated with a cumulative probability of 0.08 is approximately -1.405.

Now, to find the reading that separates the rejected thermometers, we'll use the formula:

x = μ + zσ

where x is the reading we're looking for, μ is the mean (0∘C), z is the z-score (-1.405), and σ is the standard deviation (1.00∘C).

Plugging in the values, we have:

x = 0 + (-1.405) * 1.00

x ≈ -1.405

So, the reading that separates the rejected thermometers from the others is approximately -1.405∘C. Those thermometers better cool down if they want to be accepted!

To find the reading that separates the rejected thermometers from the others, we need to find the value of the reading that corresponds to the 8th percentile.

Step 1: Convert the percentile to a z-score.
Since the readings are normally distributed with a mean of 0∘C and a standard deviation of 1.00∘C, we can find the z-score using the standard normal distribution table.

Step 2: Look up the z-score in the standard normal distribution table.
The percentile of 8% corresponds to a z-score of -1.405. So, the reading that separates the rejected thermometers from the others is -1.405 standard deviations below the mean.

Step 3: Convert the z-score back to the original units.
To convert the z-score back to the original units, we multiply it by the standard deviation and add the mean.
Reading = (z-score * standard deviation) + mean
= (-1.405 * 1.00) + 0
= -1.405

Therefore, the reading that separates the rejected thermometers from the others is -1.405∘C.

To find the reading that separates the rejected thermometers from the others, we need to determine the value of the temperature that corresponds to the 8th percentile of the normal distribution with a mean of 0∘C and a standard deviation of 1.00∘C.

The 8th percentile corresponds to the z-score which separates the lower 8% of the distribution from the rest. To find this z-score, we can use the standard normal distribution table or a statistical calculator.

Using the standard normal distribution table, we look for the z-score that corresponds to an area of 0.08 to the left. We find that the z-score is approximately -1.41.

Now, we can use the formula for converting z-scores to actual values in the normal distribution:

z = (x - μ) / σ

Where:
z = z-score
x = actual value
μ = mean
σ = standard deviation

Plugging in the values, we have:

-1.41 = (x - 0) / 1.00

Solving for x, we get:

x = -1.41 * 1.00 + 0
x = -1.41

Therefore, the reading that separates the rejected thermometers from the others is approximately -1.41∘C.

Draw a sketch of what you want, similar to this:

http://prntscr.com/8kitsp

THen look up the standard normal distribution table (left tail) the number of standard deviations that correspond to 92%. (it should be between 1.4 and 1.5).
Since each standard deviation corresponds to 1°, so you can figure out the cut-off temperature.