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 thermometers reveal that at the freezing point of water, some give readings below 0 degree C (denoted by negative numbers) and some give readings above 0 degree C (denoted by positive numbers). Assume that the mean reading is 0 degree C and the standard deviation of the readings is 1.00 degree C. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information. 7) If 9% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others. (8) If 9% of the thermometers are rejected because they have readings that are too low, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others. Assume that X has a normal distribution, and find the indicated probability. (9) The mean is mu = 60.0 and the standard deviation is sigma = 4.0. Find the probability that X is less than 53.0. (10) In one region, the September energy consumption levels for signal-family homes are found to be normally distribution with a mean of 1050 kWh and a standard deviation of 218 k Wh. Find P_45, which is the consumption level separating the bottom 45% from the top 55%.

Explanation / Answer

Question-7

We have to find x0 such that P(X>x0)=0.09 or P(X<x0)=1-0.09=0.91

So, x0=1.34 using excel function =norminv(0.91,0,1)

Question-8

We have to find x0 such that P(X<x0)=0.09

So, x0=-1.34 using excel function =norminv(0.09,0,1)

Question-9

P(X<53)= 0.0401    using excel function =NORMDIST(53,60,4,TRUE)

Question-10

We have to find P45 such that P(X<P45)=0.45

So, P45=1022.61   using excel function =norminv(0.45,1050,218)

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