Question

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

Answer 1

Answer:

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 $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 $\mu = 0, \sigma = 1$.

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 $Z = -1.75$.

$Z = \frac{X - \mu}{\sigma}$

$-1.75 = \frac{X - 0}{1}$

$X = -1.75$

The correct answer is:

D. -1.75°C