Assignment – Module 2
1. (a) Obtain the area under the standard normal curve for following cases
i. Between z = -0.7 and z = 0
ii. z < 0.8
iii. Between z = -1.2 and z = 2.4
(b) Obtain ‘z’ from standard normal curve, such that P[Z < z] = 0.75
2. The monthly flow of a stream is assumed to follow normal distribution with mean of 280
m3/sec and standard deviation of 75 m3/sec.
i. Obtain the probability of the flow being greater than 200 m3/sec and less than 350
m3/sec.
ii. Obtain the probability of flow being less than 50 m3/sec.
iii. Obtain the probability of flow being greater than 500 m3/sec.
3. A random variable X is assumed to follow normal distribution with following
probabilities.
P[X < 10] = 0.1 and P[X < 30] = 0.85
Obtain the mean and standard deviation of the random variable.
4. The annual rainfall ‘X’ is assumed to follow normal distribution over a basin with mean
100 mm and standard deviation 70 mm. Annual runoff ‘Y’ (in mm) from the basin is
related to annual rainfall by Y = 1.5X – 30 (for X > 20mm)
i. Determine the mean and standard deviation of annual runoff.
ii. Obtain the probability that the annual runoff will exceed 80 mm.
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