In January 2017 a flood with very high water level was reported at the port. It

ID: 3305483 • Letter: I

Question

In January 2017 a flood with very high water level was reported at the port. It was warned that you expect the water level to be 20 cm above the brewery. Let's assume that water level above the bridge edge in this flood, X, is normalized, ie X ~ N (20, ). Assume further that the standard deviation, = 4.5 cm.

a) The flood was 10 cm lower than expected. What is the probability that a flood will be 10 cm or more below the expected water level with the assumptions of distribution here?

b) Find a 95% dispersion range for the water level. Explain what the range gives, preferably by drawing a figure.

c) The meteorologists wish to provide a forecast for the water level in the flood expected, so that the following requirements are met. The forecast is a value, k cm. The probability that the water level in the turret is less than k shall not exceed 0.05. What is the forecast k?

d) Suppose now that the expected water level is unknown and equal to . What do we need to set up a 95% condensation range for the expected water level.

Explanation / Answer

Answer:

a) The flood was 10 cm lower than expected. What is the probability that a flood will be 10 cm or more below the expected water level with the assumptions of distribution here?

Z value for 10, z =(10-20)/4.5 = -2.22

P( x>10) = P( z > -2.22)

= 0.9868

b) Find a 95% dispersion range for the water level. Explain what the range gives, preferably by drawing a figure.

95% dispersion range is 2 sd range.

The range is (11, 29).

lower tail z value for 0.05 is -1.645.

k=20-1.645*4.5

=12.5975 cm

d) Suppose now that the expected water level is unknown and equal to . What do we need to set up a 95% condensation range for the expected water level.

Confidence Interval Estimate for the Mean

Data

Population Standard Deviation

4.5

Sample Mean

Sample Size

Confidence Level

95%

Intermediate Calculations

Standard Error of the Mean

4.5000

Z Value

1.9600

Interval Half Width

8.8198

Confidence Interval

Interval Lower Limit

11.18

Interval Upper Limit

28.82