Question
please show all work
1. Asample size of 300 collected on the random variable, x yields a mean of 60, a standard deviation of 15, and a coefficient of skew of 0.001. Assume a normal distribution a) Determine the probability that x 325. b) Determine the interval probability of x 44 and x 366. 2. Assume that the random variable. x represents the time between rainfall events in Washington DC. a) What is the appropriate population density function for making probability statements. Give the formula for the pop pdf b) If the calibrated population parameter is 5, what is the best estimate for the random variable, x What is the measure of error on the best estimate for the random vari able. 3. Given the following regression equation y a) What is the name of the method of calibration b) Illustrate the first step necessary to calibrate this model. 4. Given the following calibrated regression equation y 2+7N est the significance of the variable, if the variance of its regression coefficient is 9. Assume a sample size of 30 and an a 10% b) If the comelation coefficient between the criterion variable and the predictor variable is equal to 0.88, what is the coefficient of determination for the regression uation?
Explanation / Answer
1)
a) z=(x-)/
=(25-60)/15
=-2.33
Looking at the z-table, we get the value of 0.0099. Hence, the probability is 0.99%.
b)
z=(x-)/
=(44-60)/15
=-16/15=-1.07
z=(x-)/
=(66-60)/15
=6/15=0.4
Looking at the z-table, we get the value of 0.1423 for -1.07 and 0.6554 for 0.4. Hence, the probability of them being in between is 0.6554-0.1423=0.5131.
