The figure is shown below
From the figure
Angle 150 degree and angle p forms angles on a straight
Since the sum of angles on a straight line equals 180 degrees
Hence
Solve for p in the equation
Hence, p = 30
From the figure
Angle p and angle q are vertically opposite angles
Since vertically opposite angles are equal then
Hence, q = 30
Applying the rule of angles on a straight line
This implies
Substitute q = 30 into the equation
Solve for w
Hence, w = 90
Answer:
And we can find this probability using excel or the normal standard tabe and we got:
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:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using excel or the normal standard tabe and we got: