Question

Assume that during a quality assurance test under controlled conditions, readings on a certain type of thermometer are normally distributed with a mean of 0.00 °C and a standard deviation of 1.00 °C. Assume that as a result of the test, 3 percent of all thermometers produced will be rejected because they display temperature readings that are too high and a further 3 percent will be rejected because they display readings that are too low; the remaining 94 percent will be accepted. Find the two cut-off readings that separate the accepted thermometers from those that are rejected. Round your answers to two decimal places; add trailing zeros as needed. Only thermometers with test readings between ___°C and ___°C will be accepted.

Answer 1

Solution :

Using standard normal table,

P(Z < -1.88) = 0.03

z = -1.88

Using z-score formula,

x = z * +

x = -1.88 * 0 + 1 = -1.88

Only thermometers with test readings between -1.88 °C and 1.88 °C will be accepted .

P(Z > 1.88) = 0.03

z = 1.88

x = 1.88 * 0 + 1 = 1.88