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 2.06 and negative 1.43 and draw a sketch of the region.

Answer 1

Answer:

$P(-2.06$

And we can find this probability with this difference:

$P(-2.06$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the temperatures of a population, and for this case we know the distribution for X is given by:

$X \sim N(0,1)$  

Where $\mu=0$ and $\sigma=1$

We are interested on this probability

$P(-2.06$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(-2.06$

And we can find this probability with this difference:

$P(-2.06$