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.
1 answer:
Answer:
The two readings that are cutoff values are T=1.84 deg C and T=-1.84 deg C.
Step-by-step 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.
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