The precision scientific instrument company manufactures thermometers that are supposed to give readings of 0degrees°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 0degrees°c (denoted by negative numbers) and some give readings above 0degrees°c (denoted by positive numbers). assume that the mean reading is 0degrees°c and the standard deviation of the readings is 1.00degrees°c. also assume that the frequency distribution of errors closely resembles the normal distribution. a thermometer is randomly selected and tested. a quality control analyst wants to examine thermometers that give readings in the bottom 4%. find the temperature reading that separates the bottom 4% from the others. round to two decimal placesa. -1.48°cb. -1.89°cc. -1.63°cd. -1.75°c

D. -1.75°C

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Assume that the mean reading is 0degrees°C and the standard deviation of the readings is 1.00degrees°C. This means that .

Find the temperature reading that separates the bottom 4% from the others.

The bottom 4% if the 4th percentile.

This is the value of X when Z has a pvalue of 0.04. This is .

The correct answer is:

D. -1.75°C

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step-by-step explanation: