Question

assume the readings on thermometers are normally distributed with a mean of 0°c and a standard deviation of 1.00°c. find the probability that a randomly selected thermometer reads between -1.41 and -0.79. sketch the region. choose the correct graph below. click to view page 1 of the table. click to view page 2 of the table. the probability is \square. (round to four decimal places as needed.)

Explanation:

Step1: Identify the distribution and parameters

The readings are normally distributed with mean $\mu = 0$ and standard deviation $\sigma = 1.00$. We need to find $P(-1.41 < Z < -0.79)$ where $Z$ is the standard normal variable.

Step2: Recall the property of normal distribution

For a standard normal distribution, $P(a < Z < b) = P(Z < b) - P(Z < a)$.

Step3: Find $P(Z < -0.79)$ and $P(Z < -1.41)$ using Z - tables

• From the Z - table, $P(Z < -0.79)$: Looking up - 0.7 in the left - hand column and 0.09 in the top row, we get 0.2148.
• From the Z - table, $P(Z < -1.41)$: Looking up - 1.4 in the left - hand column and 0.01 in the top row, we get 0.0793.

Step4: Calculate the probability

Using the formula $P(-1.41 < Z < -0.79)=P(Z < -0.79)-P(Z < -1.41)$

Substitute the values: $0.2148 - 0.0793=0.1355$

Answer:

0.1355