Questions: 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 greater than 0.955°C. P(Z>0.955)=

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 greater than 0.955°C.

P(Z>0.955)=

Transcript text: Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of $0^{\circ} \mathrm{C}$ and a standard deviation of $1.00^{\circ} \mathrm{C}$. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than $0.955^{\circ} \mathrm{C}$. \[ P(Z>0.955)= \] $\square$

Solution

Solution Steps

Step 1: Standardize the Variable

To find the probability of obtaining a reading less than -0.955, we first standardize the value using the formula $Z = \frac{x - \mu}{\sigma}$. Substituting the given values, we get $Z = \frac{-0.955 - 0}{1} = -0.955$.

Step 2: Use the Standard Normal Distribution Table or Computational Tool

Next, we use the standard normal distribution to find $P(Z < -0.955)$. Using a computational tool, we find that $P(Z < -0.955) = 0.17$.