Assume that the readings at freezing on a bundle 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 less than 2.156°C.
To find the probability of obtaining a reading less than 2.156°C, we need to calculate the cumulative distribution function (CDF) at that value using the standard normal distribution.
The z-score is calculated using the formula:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
In this case, x = 2.156°C, μ = 0°C, and σ = 1.00°C.
z = (2.156 - 0) / 1.00
= 2.156
Using a z-table or a calculator, we can find the CDF at z = 2.156.
The CDF is the probability of obtaining a value less than or equal to the given z-score.
From the z-table or calculator, the CDF at z = 2.156 is approximately 0.9842.
Therefore, the probability of obtaining a reading less than 2.156°C is approximately 0.9842 or 98.42%.