Probability Distribution

The time to pass through a security screening at an airport follows an exponential distribution. The mean time to pass through the security screening is 15 minutes. To catch the flight, a passenger must clear the security screening within 18 minutes. The Probability that the passenger will miss the flight is ______________.

Suppose that the service life, in years, of a hearing aid battery is a random variable having a Weibull distribution with α=1/4 and β=2. The probability that a battery will be operating after 4 years is _____________.

Two different types of paint are compared in independent experiments. Eighteen specimens are painted using type A, and the drying time, in hours, is recorded for each. The same is done with type B. The population standard deviations are both known to be 1.0. If mean drying time is equal for the two types of paint, then P XA- XB >0.5= _____________, where XA and XB are average drying times for samples of size 18.

The daily amount of coffee, in liters, dispensed by a machine located in an airport lobby is a random variable X having a continuous uniform distribution with A = 7 and B = 11. The probability that on a given day the amount of coffee dispensed by this machine will be at most 8.8 liters given that it has already dispensed 7.8 liters is _______________.

If X is normally distributed with mean 10 and P(X>13)=0.0669, then the variance of X is _______________________. (Given that P(Z≤1.5)=0.9331)

The average teacher's salary in Karnataka is rupees 52,174. Suppose that the distribution is normal with standard deviation rupees 9500. If we sample 100 teachers' salaries, then the probability that the sample mean is less than rupees 50,000 per year is _____________.

Suppose the true value of the president's approval rating is 56%. The probability that a sample of 800 people would find a proportion between 53% and 58% is ______________.