Answer:

And we can find this probability using the normal standard table or excel and we got:

The figure shows the calculation for this case.
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 hardness 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 the normal standard table or excel and we got:

The figure shows the calculation for this case.
Answer:
<u>It</u><u> </u><u>is</u><u> </u><u>(</u><u>x</u><u> </u><u>-</u><u> </u><u>3</u><u>)</u><u>³</u><u> </u><u>-</u><u> </u><u>9</u><u>x</u><u>(</u><u>3</u><u> </u><u>-</u><u> </u><u>x</u><u>)</u>
Step-by-step explanation:
Express 27 in terms of cubes, 27 = 3³:

From trinomial expansion:

open first two brackets to get a quadratic equation:

expand further:

take y to be 3, then substitute:

The probability the pitch over the plate is a ball is 5:10. (5 balls and 10 strikes over the plate) should be written as 5:15 or 1:3 so this one is inaccurate.
Step-by-step explanation:
Rs8,100 / (Rs45 per square meter)
= 180 square meters.
The area of the 4 walls of the room is 180 sq.m.
P(G) is 26/52
P(H) is 8/52
See the rest in the photo