The Precision Scientific Instrument Company manufactures thermometers that are s

Question

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0 degree C at the freezing point of water. Tests on a large sample of these instruments revel that at the freezing point of water, some thermometers give readings below 0 degree and some give readings above 0 degree. Assume that the mean reading is 0 degree C and the standard deviation of readings is 1.00 degree C. Also assume that the readings are normally distributed. Step 1: If one thermometer is randomly selected, find the probability that, at the freezing point of water, the reading is less than 1.27 degree, We determine the probability by finding the area under the curve below z = 1.27, which is the probability of randomly selecting a thermometer with a reading less than 1.27 degree. Using Excel fx Statistical NORM.S.DIST determine the probability of selecting a thermometer with a reading less than 1.27 degree, (z = -1.27, cumulative = 1) P(z a) = ____ What percent of the thermometers will have readings above -1.23 degree ? ____% Step 3: Using Excel f Statistical NORM.S.DIST determine the probability of selecting a thermometer with a reading between -2.00 degree and 1.50 degree. P(1.50 degree z) = ____ P(-2.00 degree z) = ___ P(-2.00 degree

Explanation / Answer

1) P(Z < 1.27) = 0.8980 = 89.8%

2) P(Z > -1.23) = 1 - P(Z < -1.23) = 1 - 0.1093 = 0.8907 = 89.07%

3) P(Z < 1.5) = 0.9332

P(Z < -2) = 0.0228

P(-2 < Z < 1.5) = P(Z < 1.5) - P(Z < -2)

                        = 0.9332 - 0.0228

                        = 0.9104

                        = 91.04%

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