The Standard Normal Distribution

Question

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested.

Find the probability of obtaining a reading between -2.127°C and -2.119°C. 

Answer 1

The Probability of obtaining a reading between -2.127°C and -2.119°C is the same as the Probability of obtaining a reading between 2.119°C (≈ 2.12) and 2.127°C (≈ 2.13). A Table Of Proportions Of Area Under The Standard Normal Curve gives Area values for 2.13 and 2.12 of 0.4834 and 0.4830, respectively.

P(-2.127<Z<-2.119) is then (0.4834 - 0.4830) or 0.0004.

Since the Mean is 0 and the Standard Deviation is 1 in this case, computing the Z-value by (X - Mean) ÷ (Standard Deviation) gives Arguments or "Look-Up Values" for the table above that are the same as the Raw Data given, |-2.119| and |-2.127|.

Using a Calculus-based Formula with the Casio Programmable Calculator gives a highly accurate result of

0.0003351918782 ≈ 0.0003.