Question

In: Statistics and Probability

There is a river whose average daily flow Q follows a normal distribution. The average flow...

There is a river whose average daily flow Q follows a normal distribution. The average flow is 8000 cfs and the standard deviation is 1000 cfs. Determine the following:
(a) The probability that the flow observed on a given day exceeds 10,000 cfs.
(b) The probability that the observed flow is between 5,000 and 7,000 cfs.
(c) The value of the flow that has a 1% probability of exceeding.

Solutions

Expert Solution


Related Solutions

There is a river whose average daily flow Q follows a normal distribution. The average flow...
There is a river whose average daily flow Q follows a normal distribution. The average flow is 800 cfs and the standard deviation is 1000 cfs. Determine the following: (a) The probability that the flow observed on a given day exceeds 10,000 cfs. (b) The probability that the observed flow is between 5,000 and 7,000 cfs. c) The value of the flow that has a 1% probability of exceeding.
The flow in a river can be modeled as a log-normal distribution. From the data, it...
The flow in a river can be modeled as a log-normal distribution. From the data, it was estimated that, the probability that the flow exceeds 1100 cfs is 50% and the probability that it exceeds 100 cfs is 90%. Let X denote the flow in cfs in the river. Flood conditions occur when flow is 5000 cfs or above. To compute the percentage of time flood conditions occur for this river, we have to find, P(X≥5000)=1-P(Z<a). What is the value...
The average MCAT score follows a Normal distribution, with a mean of μ = 508 and...
The average MCAT score follows a Normal distribution, with a mean of μ = 508 and a standard deviation of σ = 8. What is the probability that the mean IQ score of 100 randomly selected people will be more than 510?
The average rainfall during the month of April follows a normal distribution with a mean of...
The average rainfall during the month of April follows a normal distribution with a mean of 5 in. and a standard deviation of 0.6 in. What is the probability that the rainfall in April will be less than 4 in.?
A factory produces steel cables, whose resilience follows a normal distribution of unknown mean and standard...
A factory produces steel cables, whose resilience follows a normal distribution of unknown mean and standard deviation σ = 10 KJ / m3. A sample of 100 pieces was taken and through a statistical study a confidence interval (898.04 - 901.96) was obtained for the average resilience of the steel cables produced in the factory. a) Calculate the value of the average resilience of the 100 pieces of the sample. b) Calculate the confidence level with which this interval has...
using 625 trading days of data, you estimated the daily log return follows a normal distribution...
using 625 trading days of data, you estimated the daily log return follows a normal distribution with a mean of 5 bps and and a stdev of 125 bps. Q1a. based on information above, what is the probability of true daily log return average is 0? can you reject the true mean is 0? can you reject the true mean is 10 bps? Q1b. what is the 90, 95, and 99% confidence interval for your mean return estimate? Q1c. what...
The daily market return follows a Normal distribution with mean 0.08/252 and standard deviation 0.15/?252. The...
The daily market return follows a Normal distribution with mean 0.08/252 and standard deviation 0.15/?252. The risk-free rate is 0.02. CAPM Betas of stock A and B are 2.1 and 0.5, respectively. All alphas are zero. Idiosyncratic volatilities of stock A and B are 0.12/?252 and 0.14/?252, respectively. The current price of stock A and B are $100/share and $200/share, respectively, and you sell short them. Initial margin rate is 50% and the maintenance margin is 30%. Compute probability that...
The distribution of ages of all the employees in Company X follows a normal distribution. The...
The distribution of ages of all the employees in Company X follows a normal distribution. The average age is 40 and the standard deviation is 5. Find the Z-score of a 50 year old employee. What is the probability that a randomly chosen employee will be younger than 35 years? What is the probability that a randomly chosen employee will have an age between 35 and 45 years? What is the probability that a randomly chosen employee will be older...
The diameter of a cylinder follows a normal distribution with the mean of 10cm and the...
The diameter of a cylinder follows a normal distribution with the mean of 10cm and the variance of 0.04 cm^2. a) Construct a Shewhart chart to monitor the process mean of cylinder diameter with a sample size 9? (Use L=3) b) If the mean of the process changes to 10.5 cm, what is the probability that you detect this mean shift at the immediate next sample (the first sample after the mean shift)? c) Continue b), what is the probability...
Assume that the life of an engine follows a normal distribution with an average life of 12 years and a standard deviation of 2 years
Assume that the life of an engine follows a normal distribution with an average life of 12 years and a standard deviation of 2 years. The seller replaces all engines that fail during the warranty period without additional charges.a) If the manufacturer wishes to replace only 1% of the engines it sells, what is the warranty time it must offer?b) supposes that Puerto Rico sold 30 engines, what is the percentage of probability that more than 1 customer will claim...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT