The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0degreesC 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 0degreesC ​(denoted by negative​ numbers) and some give readings above 0degreesC ​(denoted by positive​ numbers). Assume that the mean reading is 0degreesC and the standard deviation of the readings is 1.00degreesC. 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 places. Find P40, the 40th percentile.a)-0.57 degrees B) 0.57degrees C) 0.25 degrees D) -0.25 degreesFind Q3, the third quartile.a) 0.67 degrees B) 0.82 degrees C) -1.3 degrees D) 0.53 degrees

Answer:The value that separates the bottom 4% is -1.75; the 40th percentile is D. -0.25 degrees; Q3 is A. 0.67 degrees.Step-by-step explanation:The bottom 4% has a probability of 4% = 4/100 = 0.04.  Using a z-table, we find the value closest to 0.04 in the cells of the chart; this is 0.0401.  This corresponds to a z value of -1.75.  The formula for a z score is[tex]z=\frac{X-\mu}{\sigma}[/tex]Substituting our values for z, the mean and the standard deviation, we have-1.75 = (X-0)/1X-0 = X, and X/1 = X; this gives us-1.75 = X.The 40th percentile is the value that is greater than 40% of the other data values.  This means it has a probability of 0.40.  Using a z-table, we find the value closest to 0.40 in the cells of the chart; this is 0.4013.  This corresponds to a z value of -0.25.Substituting this into our formula for a z score along with our values for the mean and the standard deviation,-0.25 = (X-0)/1X-0 = X, and X/1 = X; this gives us-0.25 = X.Q3 is the same as the 75th percentile.  This means it has a probability of 0.75.  Using a z-table, we find the value closest to 0.75 in the cells of the chart; this is 0.7486.  This corresponds to a z value of 0.67.Substituting this into our z score formula along with our values for the mean and the standard deviation,0.67 = (X-0)/1 X-0 = X and X/1 = X; this gives us0.67 = X.