The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°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°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°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.

​If 6.3% of the thermometers are rejected because they have readings that are too high and another 6.3% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others.


–1.46° , 1.46°


–1.39° , 1.39°


–1.53° , 1.53°


–1.45° , 1.45°

Answer:

-1.53 , 1.53

Step-by-step explanation:

It is basically asking you to find the percentiles. so for the bottom 6.3% you would type into your calculator 2nd, VARS, invNorm, area: .063, mean: 0, and Standard Deviation: 1 which gives you -1.53.

for the upper 6.3% you have to take 1-.063=.937 to get the upper percentile. now type into your calculator 2nd, VARS, invNorm, area: .937, mean: 0, and Standard Deviation: 1 which gives you 1.53.

Using the normal distribution, it is found that the third quartile of Q3 is 0.67, hence option B –1.39°, 1.39° is correct.

Normal usually refers to the word "normal" in a normal distribution.

The word normal is used when something occurs that has occurred frequently. The normal distribution is somewhat similar where the main observation (mean or its surrounding) occurs frequently and as we go far from the mean, its chances decrease.

In a normal distribution with mean μ and standard deviation  σ, the z-score of a measure X will be;

Z = (X - μ)/  σ

After finding the z-score, we have to find the p-value associated with this z-score, which is the percentile of X.

The mean is 0ºC, μ= 0

The standard deviation is 1ºC, σ = 1.

Therefore when Z has a p-value of 0.75, hence X when Z = 0.67.

Z = (X - μ)/  σ

0.67 = (X - 0)/  1

X = 0.67

Thus, the two readings that are cutoff values separating the rejected thermometers from the others are B –1.39°, and 1.39°.

Learn more about normal distribution here:

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