Question

Assume that the readings at freezing on a batch of thermometers are normally distributed with a

mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and
tested.
If 1.4% of the thermometers are rejected because they have readings that are too high and another
1.4% are rejected because they have readings that are too low, find the two readings that are cutoff
values separating the rejected thermometers from the others.
interval of acceptable thermometer readings
=
°C

Answer 1

Answer: The interval of acceptable thermometer readings is -2.33°C to 2.33°C.

Step-by-step explanation: To find the cutoff values separating the rejected thermometers from the others, we use the standard normal distribution table.

Since 1.4% of the thermometers are rejected because they have readings that are too high and another 1.4% are rejected because they have readings that are too low, we can find the cutoff values by finding the z-scores that correspond to 0.014 and 0.986 in the standard normal distribution table.

The z-score corresponding to 0.014 is -2.33 and the z-score corresponding to 0.986 is 2.33.

To find the actual temperature values, we use the formula:

x = μ + zσ

where x is the temperature value, μ is the mean (0°C), z is the z-score (-2.33 or 2.33), and σ is the standard deviation (1.00°C).

So the two readings that are cutoff values separating the rejected thermometers from the others are:

-2.33°C and 2.33°C

Hope this helps, and have a great day!