Question

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees 0° and standard deviation of 1.00 degrees °C. Assume 3 3​% of the thermometers are rejected because they have readings that are too high and another 3 3​% 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.

Answer 1

The two readings that are cutoff values are T=1.84 deg C and T=-1.84 deg C.

Explanation:

Thermometers rejected by measurements above normal represent 3.3% of the total, which indicates, by normal probability distribution data, that accepted thermometers are 96.7% likely to measure less than the maximum allowable temperature.

This value (P(X>x)=0.967) corresponds to z = 1.8388. Since the mean and standard deviation values are the same as the standard normal probability distribution (mean = 0, sd = 0), the z value is equivalent to the measured value (temperature).

Given the symmetry of the probability distribution, we can affirm that the thermometers rejected by measurements below the permissible measured a temperature lower than -1.8388.