# Probability of 20ml of rainfall when 13ml chance is 87.7% and 16.9ml chance is 40.9%

Farmers in District D know when to plant and harvest because rainfall follows a particular pattern which repeats itself every seven months. Weather records for this particular area indicate a normal distribution as far as rainfall is concerned. The records further reveal that the chances of at least 13.4 millimeters of rainfall have remained at 87.7%, while the chances of at most 16.9 millimeters remain at 40.9%. For the farmers to plant wheat they need at least 20 millimeters of rainfall, with what probability do they plant the wheat? SHOW ME HOW TO WORK THIS OUT! THANK YOU!

 ROLCAM Posts: 1,437, Reputation: 250 Ultra Member #2 Oct 15, 2009, 05:06 AM
This works out as follows:-
(by extrapolation in reverse).
(based on the heading details which varies from the details in the bulk of the question)

Number

1 13.0 87.7
2 13.1 86.5
3 13.2 85.3
4 13.3 84.1
5 13.4 82.9
6 13.5 81.7
7 13.6 80.5
8 13.7 79.3
9 13.8 78.1
10 13.9 76.9
11 14.0 75.7
12 14.1 74.5
13 14.2 73.3
14 14.3 72.1
15 14.4 70.9
16 14.5 69.7
17 14.6 68.5
18 14.7 67.3
19 14.8 66.1
20 14.9 64.9
21 15.0 63.7
22 15.1 62.5
23 15.2 61.3
24 15.3 60.1
25 15.4 58.9
26 15.5 57.7
27 15.6 56.5
28 15.7 55.3
29 15.8 54.1
30 15.9 52.9
31 16.0 51.7
32 16.1 50.5
33 16.2 49.3
34 16.3 48.1
35 16.4 46.9
36 16.5 45.7
37 16.6 44.5
38 16.7 43.3
39 16.8 42.1
40 16.9 40.9
41 17.0 39.7
42 17.1 38.5
43 17.2 37.3
44 17.3 36.1
45 17.4 34.9
46 17.5 33.7
47 17.6 32.5
48 17.7 31.3
49 17.8 30.1
50 17.9 28.9
51 18.0 27.7
52 18.1 26.5
53 18.2 25.3
54 18.3 24.1
55 18.4 22.9
56 18.5 21.7
57 18.6 20.5
58 18.7 19.3
59 18.8 18.1
60 18.9 16.9
61 19.0 15.7
62 19.1 14.5
63 19.2 13.3
64 19.3 12.1
65 19.4 10.9
66 19.5 9.7
67 19.6 8.5
68 19.7 7.3
69 19.8 6.1
70 19.9 4.9
71 20.0 3.7

Conclusion a 20 millimeters has a 3.7%
Probability.
 Chris-infj Posts: 31, Reputation: 15 Junior Member #3 Oct 15, 2009, 08:20 AM
Let X be the amount of rainfall in mm

It is given that X follows a normal distribution. What is not known is the mean and the standard deviation of rainfall.

You're given $P(X \geq 13.4mm)$ = 0.877.

1. Draw a bell-shaped curve and illustrate that.

2. Then look up in a standard normal table and find the z value that corresponds to a p value of 0.877.

3. Is it a positive z or a negative value? You'll know when you look at your drawing. In fact, it is strongly advised to draw a picture.

4. So then you use the formula $\Large z = \frac{x - \mu}{\sigma}$ to obtain a first equation involving $\mu$ and $\sigma$.

Repeat as from step 1. For the other piece of information $P(X \leq16.9)$ = 0.409.

Draw a picture for that too. Look up the z value corresponding to a p value of 0.409 in normal tables or use Excel Norminv function.

You should get two simultaneous equations with $\mu$ and $\sigma$ as two unknowns and solve to get them.

Then armed with these values, you can calculate $P(X \geq 20mm )$ .
 Unknown008 Posts: 8,147, Reputation: 3745 Uber Member #4 Oct 15, 2009, 11:15 AM
Do we do these in the S2 paper?
 Chris-infj Posts: 31, Reputation: 15 Junior Member #5 Oct 16, 2009, 07:07 AM
Quote:
 Originally Posted by Unknown008 Do we do these in the S2 paper?
S1 paper
 Unknown008 Posts: 8,147, Reputation: 3745 Uber Member #6 Oct 17, 2009, 08:15 AM
Ok...

## Check out some similar questions!

Is there still a chance? [ 37 Answers ]

When two people break up because of circumstances, not because they lost feelings for each other. Is there a chance that they will get back together eventually? My boyfriend and I broke up because of circumstances, I tried to convince him out of it, but it has been so far unsuccessful. I told...

My last chance! [ 4 Answers ]

I need to know the name of a movie from the late 70's early 80's. It was about a black family held hostage by convicts. The Father was a preacher. They beat him with the bible. The little kid had a friend and their password for help was hotdog. It had something to do with tables turning. The...

Help. Do I take a chance? [ 2 Answers ]

Hi I'm a 21 year old girl, who 2 1/2 years ago started dating a 23 year bloke called Tom. Everything was perfect with him as he was honest, kind and real gentleman to me. We lasted 4 months as he didn't know what he wanted and wanted to be single again. I was devastated as you can imagine as this...

2nd chance? [ 7 Answers ]

My boyfriend of 2 years recently dumped me. The thing is, he kept changing his reason. It makes me think he's confused. He left me once before, and I did the whole beg and plead thing which did not work, and after breaking off all contact and ignoring him, he came back because he loved me and need...