What are the cutoff values?

Question

Assume that the readings on the thermometers are normally distributed with a mean of 0° and standard deviation of 1.00°C. Assume 3.2​% of the thermometers are rejected because they have readings that are too high and another 3.2​% are rejected because they have readings that are too low. Draw a sketch and find the two readings that are cutoff values separating the rejected thermometers from the others.

I have found the graph but am having a hard time find the cutoff values.

Answer 1

See if these hints get you pointed in the right direction.

1) This is, essentially, a confidence interval problem. You need to find a 100 - (3.2)*2 = 93.6% confidence interval.

1. a.) it is a two-tailed confidence interval. You will want to find the 100 - 3.2 = 96.8th percentile and the 3.2th percentile.
2. b.) You are given the info that the readings are normally distributed with a mean of 0 and a standard deviation of 1.
3. There is a famous reference distribution with a mean of 0 and a standard deviation of 1, the Z distribution, also known as the standard normal distribution. This distribution is tabled in most statistics textbooks and is available in excel as the NORM.INV, "inverse cumulative normal function". (An inverse of a function is a fancy way of saying, what used to be the answer to a question is now the input value). You will need to convert percentiles to cumulative probabilities to use the NORM.INV function in excel., e.g., 93.6 becomes 93.6/100 = .936.
4. Check back if you run into trouble or when you would like to learn how to normally distributed values on other scales to the Z score scale.