Question

Assume the readings on thermometers are normally distributed with a mean of 0degreesC and a standard deviation of 1.00degreesC. Find the probability that a randomly selected thermometer reads between negative 2.22 and negative 1.49 and draw a sketch of the region.

Answer 1

Answer:

0.0549 is the probability that the thermometer reads between -2.22 and -1.49.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 0 degrees

Standard Deviation, σ = 1 degrees

We are given that the distribution of readings on thermometers is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(thermometer reads between -2.22 and -1.49)

$P(-2.22 \leq x \leq -1.49) = P(\displaystyle\frac{-2.22 - 0}{1} \leq z \leq \displaystyle\frac{-1.49-0}{1}) = P(-2.22 \leq z \leq -1.49)\\\\= P(z \leq -1.49) - P(z < -2.22)\\= 0.0681 - 0.0132 = 0.0549$

0.0549 is the probability that the thermometer reads between -2.22 and -1.49.